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- Assessment Technique: Direction: Evaluate the following integrals. 1. S( 30x5 + 25x3 20x4 dx 3 4 8x5 2. S 15 dx 5 12x3 15 12 3. S 3arrow_forwardIntegration by Parts: Evaluate the following integrals. (Show your step-by-step solution)arrow_forwardEvaluate the definite integral. Use the integration capabilities of a graphing utility to verify your result. 2x dx + 64 Step 1 6 2x To find the definite integral dx, apply the basic integration rule. + 64 Let u = x- + 64. Differentiate u in terms of x, du = 4 X 2 x dx. Step 2 Rewrite the integration in terms of u. 9. 2x Xx=6 dx = du x + 64arrow_forward
- Use a change of variables to evaluate the following indefinite integral. 2x (x? -2) 102 dx Determine a change of variables from x to u. Choose the correct answer below. OA. u=x B. u= (x -2) 102 O B. u= %3D O C. u= 2x D. u=x -2 =X-2 Write the integral in terms of u. 2x (2 -2) 102 dx = Sa duarrow_forwardUse a change of variables to evaluate the following indefinite integral. 2x (x² - 2) 102 dx Determine a change of variables from x to u. Choose the correct answer below. O A. u=x² =(x² - 2) 10 (x² -2) 102 O B. u= O C. u=2x D. u=x- 2 Write the integral in terms of u. S2x (-2) 102 dx%3= 102 du Evaluate the integral. |2x (x -2) 102 dx%3Darrow_forwardIntegral by substitutionarrow_forward
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