Question

Evaluate the integral below by interpreting y=f(x) it in terms of areas in the figure. A1 АЗ The areas of the labeled regions are 10 31 5 A2 7A4 10 A1= 7, A2=4, A3=2 and A4=2 (figure is NOT to scale) v= 5.5" f(a)de V = Enter your answer as a whole number

Answer 1

Using the property of the definite Integral, for any c in the closed interval [a,b] and for any continuous function f(x) on [a,c], we have,

$\int_{a}^{b} f(x)dx= \int_{a}^{c} f(x)dx+ \int_{c}^{b} f(x)dx$

By expressing the area A​​​​​​3 as Integrals, we have
Аз f(x)dx 5
$\ and \ A_{4}=\int_{7}^{10}(- f(x))dx$, we have got V= A​​​​​​​​​​​​3+(-A​​​4)= 2+(-2)=0.

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