the exercises will be on file please

4. [-/0.13 Points] DETAILS SCALCET8 7.TF.003. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Determine whether the statement is true or false. x2 + 9 A x2 ( x - 9) can be put in the form - 2 x - 9 O True O False Need Help? Read It 5. [-/0.13 Points] DETAILS SCALCET8 7.4.AE.002. 0/100 Submissions Used MY NOTES ASK YOUR TEACHER Video Example () EXAMPLE 2 Evaluate 6 x 2 + 7 x - 1 dx . 2x3 + 3x2 - 2x SOLUTION Since the degree of the numerator is less than the degree of the denominator, we don't need to divide. We factor the denominator as 2x3 + 3x2 - 2x = x(2x2 + 3x - 2) = x(2x - 1)(x + 2). Since the denominator has three distinct linear factors, the partial fraction decomposition of the integrand has the form 6x2 + 7 x - 1 x(2x - 1) (x + 2) To determine the values of A, B, and C, we multiply both sides of this equation by the product of the denominators, x(2x - 1)(x + 2), obtaining 6x2 + 7x - 1 = , ( x + 2 ) + B x ( * + 2 ) + Cx ( 2 x - 1 ) . Expanding the right side of the equation above and writing it in the standard form for polynomials, we get 6x2 + 7x - 1 = (2A + B+ 20)x2 +( )X - 2A . The polynomials in the equation above are identical, so their coefficients must be equal. The coefficient of x on the right side, 2A + B + 2C, must equal the coefficient of x2 on the left side--namely, 6. Likewise, the coefficients of x are equal and the constant terms are equal. This gives the following system of equations for A, B, and C. 2A + B + 20 = 3A + 2B - C = -2A Solving, we get A = , B = , and C = , and so we have the following. (Remember to use absolute values where appropriate.) 6 x2 + 7 x - 1 dx = 2x 3 + 3x 2 - 2x 1 ) 2X 1 x2 dx + K In integrating the middle term we have made the mental substitution u = 2x - 1, which gives du = 2 dx and dx = = du. Need Help? Read It4x3 - 2x - 6 can be put in the form X - 1 + - C X - x X + B x + 1 ' , where A, B and C are constants. O True O False Need Help? Read It 2. [-/0.13 Points] DETAILS SCALCET8 7.TF.001. 0/100 Submissions Used Determine whether the statement is true or false. x(x2 + 16) can be put in the form A x + 4 + B x2 - 16 X - O True O False Need Help? Read It 3. [-/0.13 Points] DETAILS SCALCET8 7.TF.002. 0/100 Submissions Used Determine whether the statement is true or false. x2+ 36 can be put in the form A + B + x(x2 - 36) x + 6 C O True O False