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study help
mathematics
precalculus 1st

Questions and Answers of Precalculus 1st

Evaluate the following integrals. 4x² x² 1 - dx, x 7|2
Evaluate the following integrals. dx V3 - 2x - x² 2
Evaluate the following integrals. [₁ tan³ 4x dx
Evaluate the following integrals. 2 S= x + 2 2 o x² + 4x + 8 - dx
Evaluate the following integrals. X x² + 2x² + 1 X dx
Evaluate the following integrals. x sec² tan5 x S se dx
Evaluate the following definite integrals. x² In x dx
Evaluate the following integrals. 12x - 8 x4 - 2x² 2x² + 1 - dx
Evaluate the following integrals. x4 1 + x² dx
Evaluate the following definite integrals. -1/V2 0 y tany² dy
Evaluate the following integrals. do 1+ sin 0
Evaluate the following definite integrals. √3/2 1/2 sin¹y dy
Evaluate the following integrals. x² - 4 X x³ - 2x² + x dx
Evaluate the following integrals. [sec sec² x tan¹/2 x dx
Evaluate the following integrals. 9x² - 25 3 x³ -dx, x > 3
Evaluate the following integrals. [csc10 csc ¹0x cotx dx
Give the appropriate form of the partial fraction decomposition for the following functions. 2x² + 3 2 (x² - 8x + 16) (x² + 3x + 4)
Evaluate the following integrals. do 1 csc 0
Evaluate the following definite integrals. 2 J2/V3 -1 z sec z dz
Give the appropriate form of the partial fraction decomposition for the following functions. 2 x(x² - 6x + 9)
Evaluate the following integrals. 1 - x 1 - Vx dx
Evaluate the following integrals. √9-x² x² 2 dx
Give the appropriate form of the partial fraction decomposition for the following functions. 20x (x - 1)²(x² + 1)
Evaluate the following integrals. sed sec-²x tan³ x dx
Evaluate the following integrals. x² (25+x²)2 dx
Evaluate the following integrals. csc4 x feste cot² x dx
Evaluate the following integrals. dx sec x - 1
Give the appropriate form of the partial fraction decomposition for the following functions. x² x³(x² + 1)
Evaluate the following integrals. dx x²√9x² - 1 x 1 3
Evaluate the following integrals. Star tan³ 0 sec¹0 de dᎾ
Evaluate the following integrals. x² (100-x²)3/2 dx
Evaluate the following integrals. /4 sec* Ꮎ dᎾ
Evaluate the following integrals. x² + x + 2 (x + 1)(x² + 1) S dx
Evaluate the following integrals. 18(x² + 4) x(x² + 8) dx
Evaluate the following integrals. √₁ dx x³√x² 100 x > 10
Evaluate the following integrals. J dx 2 x³√x² - 1 x > 1
Evaluate the following integrals. x³ (81 - x²)2 dx
Evaluate the following integrals. 0 π/4 tan³ 0 sec² 0 de
Use integration by parts to derive the following reduction formulas. [x" ea x" eax dx = xneax a n [x² xn-leax dx, a eax dx, for a 0
Evaluate the following integrals. •w/3 Ꮭ ' 3{6 cot Ꮎ dᎾ
Evaluate the following integrals. x² + 3x + 2 x(x² + 2x + 2) -dx
Evaluate the following integrals. 2x² + 5x + 5 (x + 1)(x² + 2x + 2) - dx
Evaluate the following integrals. √ ₁ dx x(x² - 1)³/2² x > 1
Use integration by parts to derive the following reduction formulas. [x x" cos ax dx = x" sin ax a -√x²² a x"-1 sin ax dx, for a 0
Use the approaches discussed in this section to evaluate the following integrals. dx x¹/2 + x3/2
Evaluate the following integrals. z+1 2 z(z² + 4) - dz
Evaluate the following integrals. x3 (x²16) 3/2 dx, x < -4
Use integration by parts to derive the following reduction formulas. [x² x" sin ax dx = x" cos ax a n "fx- x- cos ax dx, for a 0
Evaluate the following definite integrals. S 0 dx √x² + 16
Evaluate the following integrals. 20x √(x - 1)(x²) - dx (x - 1)(x² + 4x + 5)
Use integration by parts to derive the following reduction formulas. [In -n fru- In" x dx = x ln" x - n In"-1 x dx
Evaluate the following integrals. x² X - x² + 4x - 4 3 dx
Evaluate the following definite integrals. 1 1/√3x²√1 + x² dx
Evaluate the following definite integrals. 16 dx Ли 8V2 √x² - 64 2
Use the approaches discussed in this section to evaluate the following integrals. x - 2 x² + 6x + 13 2 -dx
Evaluate the following integrals. S 1 (y² + 1)(y² + 2) -dy
Use the approaches discussed in this section to evaluate the following integrals. Jo 7/4 3V1 + sin 2x dx
Evaluate the following definite integrals. 2 1 1₁ x²√4 - x² 2 xp. dx
Use the approaches discussed in this section to evaluate the following integrals. S= dx 04-√x
Evaluate the following integrals. 12/12 x² + 4 X 2x + 1 dx
Evaluate the following integrals. "sec 4 (In 0) Ꮎ - ᎾᏢ .
Use the approaches discussed in this section to evaluate the following integrals. π/8 S." V1 - cos 4x dx
Evaluate the following integrals. Jo 0 TT/2 x sin³ (x²) dx
Use the approaches discussed in this section to evaluate the following integrals. ex e2x + 2e + 1 - dx
Evaluate the following definite integrals. •1/√3 0 √x² + 1 dx
Use the approaches discussed in this section to evaluate the following integrals. 3 2 x² + 2x + 1 2 -dx
Evaluate the following definite integrals. √2 √x² - 1 -dx X
Evaluate the following integrals. π/2 dy d sin y Jπ/6
Evaluate the following definite integrals. 10 dx 2 10/V3 Vx² - 25
Evaluate the following integrals. TT/4 TT/4 tan³ x sec² x dx
Evaluate the following definite integrals. 0 1/3 dx (9x² + 1)3/2
Find the area of the following regions. In each case, graph the relevant curves and show the region in question.The region bounded entirely by the curveand the x-axis. - 4x - 4 x² - 4x 5 X 2
Evaluate the following definite integrals. 4 dx SONS √4/√3 x²(x² - 4)
Evaluate the following integrals. TT/3 -π/3 Vsec² 0 - 1 de
Use the approaches discussed in this section to evaluate the following integrals. S 2 x³ + 3x² + 3x + 1 -dx
Evaluate the following integrals. Jo csc ¹0 x cot³ x dx 10
Evaluate the following integrals. 0 77 (1 - cos 2x)³/² dx
Evaluate the following integrals. π/4 -π/4 V1 cos 4x dx
Evaluate the following definite integrals. 6V3 9 x² 2 (x²+36) ² dx
Evaluate the following integrals. 2x² dx 12x + 36
Evaluate the following integrals. Je e* sec (e* + 1) dx
Evaluate the following integrals. TT/8 S™ 0 V1 cos 8x dx
Evaluate the following integrals. TT/2 VI cos 2x dx
Evaluate the following integrals. 0 π/4 (1 + cos 4x)³/2 dx
Evaluate the following integrals. √ *² - 2x + 1 =dx √x² - 2x + 10 2 X
Explain why the coefficients A and B cannot be found if we set x² (x-4) (x + 5) A x - 4 + B x + 5'
Evaluate the following integrals. x² + 2x + 4 √x² - 4x dx, x > 4
Resolve the apparent discrepancy between dx √ x(x - 1)(x + 2) dx √x(x - 1)(x + 2) = In (x - 1)² x + 2] |xx|³ In x + 2] 6 In |x-1| 3 + C and In |x| 2 + C.
The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals. 2x³ + x² 2 x² + x = 6 6x + 7 - dx
Use the reduction formulas in a table of integrals to evaluate the following integrals. 2x [x³e² dx
Use the reduction formulas in a table of integrals to evaluate the following integrals. x² e-3x dx
Evaluate the following integrals. x² - 8x + 16 Ja (9+ 8x - x2)3/2 x2)3/2 dx
Evaluate the following integrals. 4 dx x² - 2x + 10 2
Evaluate the following integrals. (√2+3)/(2√2) 1/2 dx 8x²8x + 11
Use the reduction formulas in a table of integrals to evaluate the following integrals. se sec4 4x dx
The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals. dx ex et + e²x 2x
The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals. √ et (e* - 1)(e* + 2) -dx
The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals. 1₁ sec 0 1 + sin de 0
The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals. cos x (sin³x - 4 sin x) -dx
The following integrals require a preliminary step such as long division or a change of variables before using partial fractions. Evaluate these integrals. [Ve Vex + 1dx

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