Question: Find the derivative. StartFraction d Over dt EndFraction Integral from 0 to t squared StartRoot u Superscript 5 EndRoot du a. by evaluating the integral
Find the derivative. StartFraction d Over dt EndFraction Integral from 0 to t squared StartRoot u Superscript 5 EndRoot du a. by evaluating the integral and differentiating the result. b. by differentiating the integral directly. Question content area bottom Part 1 a. Evaluate the definite integral. StartFraction d Over dt EndFraction Integral from 0 to t squared StartRoot u Superscript 5 EndRoot du equalsStartFraction d Over dt EndFraction left parenthesis nothing right parenthesis (Simplify your answer. Use integers or fractions for any numbers in the expression.) Part 2 Find the derivative of the evaluated integral. StartFraction d Over dt EndFraction Integral from 0 to t squared StartRoot u Superscript 5 EndRoot du equals enter your response here (Simplify your answer. Use integers or fractions for any numbers in the expression.) Part 3 b. Which of the following is the correct way to find the derivative of the given integral directly? A. Substitute t squared for u in the function in the integrand, then multiply by the derivative of t squared. B. Substitute t squared for u in the function in the integrand, then multiply by t squared. C. The function cannnot be differentiated using the Fundamental Theorem of Calculus. D. Substitute t squared for u in the function in the integrand. Part 4 Therefore, StartFraction d Over dt EndFraction Integral from 0 to t squared StartRoot u Superscript 5 EndRoot du equals enter your response here (Simplify your answer. U
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