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Chapter 4: Q. 36 (page 399)

Use the Second Fundamental Theorem of Calculus, if needed, to calculate each the derivatives expressed in Exercises 35鈥�48.
ddx鈭�2xsintt.dt

Short Answer

Expert verified

The derivative expression of ddx鈭�2xsintt.dtis sinxx.

Step by step solution

01

Step 1. Given Information.

The derivative:

ddx鈭�2xsintt.dt

02

Step 2. Second Fundamental theorem of calculus.

f is continuous on [a,b]for all x鈭�[a,b], then ddx鈭�exf(t).dt=f(x)

03

Step 3. Find the derivative expression.

By Second Fundamental theorem of calculus,

ddx鈭�2xsintt.dt=sinxx

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Most popular questions from this chapter

Use the Fundamental Theorem of Calculus to find the exact values of the given definite integrals. Use a graph to check your answer.

鈭�鈭�11鈥�2x4xdx

If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9,鈭�-23g(x)dx=2, and 鈭�36g(x)dx=3, then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.

鈭�-2-2x(f(x)+3)2dx

Read the section and make your own summary of the material.

If 鈭�-23f(x)dx=4,鈭�-26f(x)dx=9,鈭�-23g(x)dx=2and 鈭�36g(x)dx=3,then find the values of each definite integral in Exercises 29-40. If there is not enough information, explain why.

鈭�36fxdx.

Consider the region between f and g on [0, 4] as in the

graph next at the left. (a) Draw the rectangles of the left-

sum approximation for the area of this region, with n = 8.

Then (b) express the area of the region with definite

integrals that do not involve absolute values.
See all solutions

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