Find the Derivative of the Integral

Problem

d()/d(x)*(∫_0^10)((4*x2+7)*d(x))

Solution

1. Identify the nature of the expression. The expression is a definite integral with constant limits of integration, 0 and 10

2. Evaluate the definite integral. Since the integrand 4*x2+7 is integrated over a fixed interval, the result of the integral is a constant value.

3. Apply the constant rule for derivatives. The derivative of any constant with respect to x is 0

4. Conclude that since the integral does not depend on x its derivative with respect to x is zero.

Final Answer

d()/d(x)*(∫_0^10)((4*x2+7)*d(x))=0

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