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mathematics
calculus early transcendentals 9th
Calculus Early Transcendentals 9th Edition James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin - Solutions
We know thatis a continuous function by FTC1, though it is not an elementary function. The functionsare not elementary either, but they can be expressed in terms of F. Evaluate the following integrals in terms of F.a.b. F(x) = f e di
Show that if a > –1 and b > a + 1, then the following integral is convergent. a x' ах Jo 1+ x 4-
Evaluate the integral. w/6 9/- V1 + sin 20 de
Use the Table of Integrals on the Reference Pages to evaluate the integral.123 x* dx x10 – 2
Evaluate the integral. 1- tan'x dx sec'x
Evaluate the integral. 3x2 + 1 dx Jo x + x? + x + 1
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. dx x + x 8
Evaluate the integral. x? + 1 dx (x? – 2x + 2)2
Evaluate the integral.∫2π0 t2 sin 2t dt
Evaluate the integral. x³ - 2x? + 2x – 5 dx x* + 4x? + 3
Evaluate the integral. tan x sec?x dx cos x
Evaluate the integral. dx J 1 + e*
Evaluate the integral.∫π/20 cos3x sin 2x dx
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. -dx Jo X
Evaluate the integral. fxT- x* dx
Evaluate the integral.∫π0 x sin x cos x dx
Evaluate the integral. x' + 2x Jo x* + 4x? + 3
Evaluate the integral.∫ sin √at dt
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. 1 5 - x
Evaluate the integral. =/2 cos t dt Jo V1 + sin?t
Evaluate the integral. arctan(1/x) dx 3,
Evaluate the integral. x* + x - 1 dx x' + 1
Evaluate the integral. sin e + tan 0 - de cos'e
Evaluate the integral. | In(x + Vx? – 1) dx
Evaluate the integral. dx s1 + |x|
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. (14 dx J-2 x + 2
Evaluate the integral. rs M dM a. Ji
Evaluate the integral. 5x* + 7x? + x + 2 dx x(x? + 1)?
Evaluate the integral. w/2 cotx T/6
Evaluate the integral. Lle - 1|dx
Evaluate the integral. dx e*V1 - e-2*
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. J-1 (x + 1)?
Evaluate the integral. (In x)? dx x3
Evaluate the integral. x* + 3x? + 1 dx x' + 5x + 5x .3
Evaluate the integral. w/2 cot'x dx /4 3. X.
Evaluate the integral. 1 +x dx 1- x
Evaluate the integral. *In 10 e*. e"Ve* - 1 Jo e* + 8
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. xp -2 X
Evaluate the integral. 7/3 sin x In(cos x) dx Jo
Three integrals are given that, although they look similar, may require different techniques of integration. Evaluate the integrals.a.b.c. In x dx.
Use(a) The Trapezoidal Rule(b) The Midpoint Rule(c) Simpson’s Rule to approximate the given integral with the specified value of n. sin Vx dx, n = 6
Evaluate the integral. y dy (у + 4)(2у — 1)
Evaluate the integral. ax 9-x2
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. 1 dx J. x? + 4 an
Evaluate the integral. arctan x 1+ x?
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. dx =, In 15 x² – 1
Evaluate the integral.∫ (x + 2)2(x + 1)20 dx
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If ∫∞a f(x) dx and ∫∞a g(x) dx are both divergent, then ∫∞a [f(x) + g(x)] dx is divergent.
Evaluate the integral. x + 2 +3x 4 **
Use(a) The Trapezoidal Rule(b) The Midpoint Rule(c) Simpson’s Rule to approximate the given integral with the specified value of n. In(1 + e*) dx, n= 8
Evaluate the integral.∫ cot x cos2x dx
Use the Table of Integrals on the Reference Pages to evaluate the integral. coth(1/y) dy y?
Evaluate the integral. 4y? — Ту — 12 7y dy Л у(у + 2)(у — 3)
Evaluate the integral.∫ t csc2t dt
Evaluate the integral. 1/2 xV1 - 4x2 dx Jo
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. et (1 + e*)?
Evaluate the integral.∫ x2 tan–1x dx
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If∫∞a f(x) dx and ∫∞a g(x) dx are both convergent, then ∫∞a [f(x) + g(x)] dx is convergent.
Evaluate the integral.∫ t sin t cos t dt
Use(a) The Trapezoidal Rule(b) The Midpoint Rule(c) Simpson’s Rule to approximate the given integral with the specified value of n. sin t -dt, n-4 n = 4
Evaluate∫ √tan x dx.
Evaluate the integral.∫ csc5θ cos3θ dθ
Use the Table of Integrals on the Reference Pages to evaluate the integral.∫π0 x3 sin x dx
Evaluate the integral. 3t – 2 dt t +1
Evaluate the integral.∫ tan–1(2y) dy
Evaluate the integral. (2/3 * V4 - 9x2 dx Jo
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. J2 x²-1
Evaluate the integral. x? + 2 dx х + 2
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is a continuous, decreasing function on [1, ∞) andthen ∫∞1 f(x) dx is convergent. limr f(x) = 0,
Evaluate the integral. x* + 9 хр.
Use(a) The Trapezoidal Rule(b) The Midpoint Rule(c) Simpson’s Rule to approximate the given integral with the specified value of n. dx, n= п 3 10 Jo 1 + x*
Evaluate the integral.∫ sin x sec5x dx
Use the Table of Integrals on the Reference Pages to evaluate the integral. arctan /x dx
Evaluate the integral. x? dx х — 1
Evaluate the integral.∫ t4 ln t dt
Evaluate the integral. dx (x – 1)/2 1)3/2
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. x? + x + 1 -dx
Evaluate the integral. dx
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If f is continuous on [0, ∞) and ∫∞1 f(x) dx is convergent, then ∫∞0 f(x) dx is convergent.
Evaluate the integral. (2x + 1)
Use(a) The Trapezoidal Rule(b) The Midpoint Rule(c) Simpson’s Rule to approximate the given integral with the specified value of n. 1 dt, n = 10 2 In t
Evaluate the integral. S(1 + sin t) cost dt
Use the Table of Integrals on the Reference Pages to evaluate the integral. Sxv2 + x* dx
Evaluate the integral. 1 dx (x + a)(x + b)
Evaluate the integral.∫ ln √x dx
Evaluate the integral. dt tV1? - 16
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. r-3 4 - x? dx
Evaluate the integral. e2x 1+ e** ,4x
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.(a) Every elementary function has an elementary derivative.(b) Every elementary function has an elementary antiderivative.
Evaluate the integral. In(In y) dy y
Use(a) The Trapezoidal Rule(b) The Midpoint Rule(c) Simpson’s Rule to approximate the given integral with the specified value of n. Vy cos y dy, n= 8 n = 8
If 0 < a < b, find 1/t { [bx + a(1 - x)1 dx lim
Evaluate the integral.∫ √cos θ sin3θ dθ
Use the Table of Integrals on the Reference Pages to evaluate the integral. cos°e de
Evaluate the integral. 1 x(x – a)
Evaluate the integral.∫ cos–1x dx
Evaluate the integral. dx Jo (a? + x*)/2* a >0
Determine whether the integral is convergent or divergent. Evaluate integrals that are convergent. ro -dx J- (x² + 1)
Evaluate the integral. x² - 1
Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.The Midpoint Rule is always more accurate than the Trapezoidal Rule.
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