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Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

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Section
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

In Problems 33-36, evaluate each integral (a) with the Fundamental Theorem of Calculus and (b) with a graphing calculator (as a check).

2 0 x x 2 + 4 d x

(a)

To determine

To calculate: The value of the integral 02xx2+4dx using Fundamental Theorem of Calculus.

Explanation

Given Information:

The provided integral is 02xx2+4dx.

Formula used:

To calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

The value of the integral 1xdx=ln(x).

The value of the expression ln(ab)=lnalnb.

Fundamental Theorem of Calculus:

If f is a continuous function on a closed interval [a,b], then the definite integral of f exists and its value is abf(x)dx=F(b)F(a) where F is a function such that F(x)=f(x) for all x in [a,b].

Calculation:

Consider the integral 02xx2+4dx.

Recall that to calculate a definite integral, evaluate the indefinite integral and then substitute the limits of the integral.

Thus, evaluate the integral.

Consider the expression (x2+4).

Differentiate with respect to x.

ddx(x2+4)=2xd(x2+4)=2xdx

Thus, d(x2+4)=2xdx.

Recall that if f is a continuous function on a closed interval [a,b], then the definite integral of f exists and its value is abf(x)dx=F(b)F(a) where F is a function such that F(x)=f(x) for all x in [a,b]

(b)

To determine

To calculate: The value of the integral 02xx2+4dx using a graphing calculator.

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Chapter 13 Solutions

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Sect-13.1 P-9ESect-13.1 P-10ESect-13.1 P-11ESect-13.1 P-12ESect-13.1 P-13ESect-13.1 P-14ESect-13.1 P-15ESect-13.1 P-16ESect-13.1 P-17ESect-13.1 P-18ESect-13.1 P-19ESect-13.1 P-20ESect-13.1 P-21ESect-13.1 P-22ESect-13.1 P-23ESect-13.1 P-24ESect-13.1 P-25ESect-13.1 P-26ESect-13.1 P-27ESect-13.1 P-28ESect-13.1 P-29ESect-13.1 P-30ESect-13.1 P-31ESect-13.1 P-32ESect-13.1 P-33ESect-13.1 P-34ESect-13.1 P-35ESect-13.1 P-36ESect-13.1 P-37ESect-13.1 P-38ESect-13.1 P-39ESect-13.1 P-40ESect-13.2 P-1CPSect-13.2 P-2CPSect-13.2 P-1ESect-13.2 P-2ESect-13.2 P-3ESect-13.2 P-4ESect-13.2 P-5ESect-13.2 P-6ESect-13.2 P-9ESect-13.2 P-10ESect-13.2 P-11ESect-13.2 P-12ESect-13.2 P-7ESect-13.2 P-8ESect-13.2 P-23ESect-13.2 P-24ESect-13.2 P-13ESect-13.2 P-14ESect-13.2 P-15ESect-13.2 P-16ESect-13.2 P-17ESect-13.2 P-18ESect-13.2 P-19ESect-13.2 P-20ESect-13.2 P-21ESect-13.2 P-22ESect-13.2 P-25ESect-13.2 P-26ESect-13.2 P-27ESect-13.2 P-28ESect-13.2 P-29ESect-13.2 P-30ESect-13.2 P-31ESect-13.2 P-32ESect-13.2 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