   Chapter 4.5, Problem 66E

Chapter
Section
Textbook Problem

Evaluating a Definite Integral In Exercises 61-68, evaluate the definite integral. Use a graphing utility to verify your result ∫ 0 2 x 1 + x 2 x 2   d x

To determine

To calculate: The definite integral 02x1+2x2dx and also verify it by using Ti-83.

Explanation

Given:

The provided integral is:

02x1+2x2dx

Formula used:

According to theorem for change of variable for indefinite integrals;

If u=g(x) then du=g'(x)

Then integral will take the following form,

f(g(x))g'(x)dx=f(u)du=F(u)+C

As according to fundamental theorem of calculus,

abf(x)dx=F(b)F(a)

Calculation:

Consider, u=1+2x2

Also, when

x=02x2=2(0)21+2x2=1+0u=1

And,

x=22x2=2(2)21+2x2=1+8u=9

Then on differentiating above equation with respect to x we get,

dudx=0+4xdu4=xdx

Convert the integral in terms of u

02x1+2x2dx

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