Question

f(x)dx=_, | f(r)dr? Given that what IS Preview answer Evaluate the integral below by interpreting it in terms of areas in the figure. The areas of the labeled regions are A1-5, A2-4, A3-2 and A4:1 y-fx) A1 АЗ A2 igure is NOT to scale Enter your answer as a whole number Evaluate dx. 1 + e1.82z 71.7 answer If -16 f(x)dx = 12 and r-16 g(x)dx = 15 J- 85 and -16 h(z)dz 21 -85 what does the following integral equal? -16 (5f(a) +2g(x) - h(z)]dx-

Answer 1

#1

$\large \int _4^{10}f(x).dx =\frac{10}{3}$

Using identity

1. | f(x)dx= | f(t)dt (t is dummy variable) rb 2. | f(x)dx=-| f(x)dx

$\large \int _4^{10}f(r).dr =\frac{10}{3}$

$\large \int _{10}^4 f(r).dr=-\int _4^{10}f(r).dr =\mathbf{-\frac{10}{3}}$

#2

$\large \int _0^5f(x)dx=A_1 - A_2 =5-4=\mathbf{1}$

(integration is represents the signed area)

#3

$\large \int _1^1 \frac{cos(x)ln(1+x^2)+x^{4.4}}{1+e^{1.82x-71.7}}=\mathbf{0}$

(because $\small \int _a^a f(x)=\mathbf{0}$ )

#4

$\small \int _{-85}^{-14} [5 f(x)+2g(x)-h(x)].dx=[5\int _{-85}^{-14} f(x).dx+2\int _{-85}^{-14}g(x).dx-\int _{-85}^{-14}h(x)dx]$

$\small =[5(12)+2(15)-21]$

$\small =\mathbf{69}$