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Chapter 3: Q. 23 (page 166)

Use the result obtained in Problem 20to find the area enclosed by f(x)=x2+3x+5, the x-axisand the lines x=-4andx=4.

Short Answer

Expert verified

The area is82.67.

Step by step solution

01

Step 1. Given information

It is given that f(x)=x2+3x+5, we need to use the result obtained in Problem 20to determine the area enclosed byf(x), thex-axisand the linesx=-4andx=4.

02

Step 2. Simplify

f(x)=x2+3x+5

For x=-4,

y0=(4)2+3路(-4)+5

=9

For x=0,

y1=(0)2+3(0)+5

=5

For x=4,

y2=(4)2+3(4)+5

=33

So, Area =23(y0+4y1+y2)

=23(9+4路5+33)

=2483

=82.67.

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