   Chapter 4.P, Problem 10P

Chapter
Section
Textbook Problem

# Find d 2 d x 2 ∫ 0 x ( ∫ 1 sin t 1 + u 4 d u )   d t .

To determine

To find:

d2dx20x1sint1+u4dudt

Explanation

1) Concept:

i) Fundamental Theorem of Calculus: If f is continuous on a, b, then the function g is defined by axftdtg is continuous and differentiable on (a, b) and g(x)=f(x).

ii) In Leibnitz notation, if y=f(u) and u=g(x) are both differentiable functions, then

dydx=dydu·dudx

2) Calculation:

By using Fundamental Theorem of Calculus,

ddx0x1sint1+u4dudt=1sinx1+u4du

Again, by using Fundamental Theorem of Calculus,

d2dx20x1sint1+u4dudt=ddx(1sinx1+u4du)

Use the chain rule to the RHS of the above equation

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