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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
BuyFindarrow_forward

Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

If f is continuous and g and h are differentiable functions, find a formula for

d d x g ( x ) h ( x ) f ( t ) d t

To determine

To find: The formula for ddxg(x)h(x)f(t)dt.

Explanation

Given information:

The functions g(x) and h(x) are differentiable functions in case of f(x) as continuous function.

Calculation:

Show the integral function as follows:

ddxg(x)h(x)f(t)dt (1)

Modify the limits.

Consider the constant a is in domain of f. Hence, the limits are modified as follows:

ddxg(x)h(x)f(t)dt=ddx[g(x)af(t)dt+ah(x)f(t)dt]=ddx[ag(x)f(t)dt+ah(x)f(t)dt]

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