Applications of Integration

The area is $2x$.

The area is $x^2$.

The area is $4x$.

The area is $\frac{1}{2}x^2$.

A function for the area of a cross-section perpendicular to the y-axis on the closed interval [b, a]

A function for the area of a cross-section perpendicular to the y-axis on the closed interval [a, b]

A function for the area of a cross-section perpendicular to the x-axis on the closed interval [a, b]

A function for the area of a cross-section perpendicular to the x-axis on the closed interval [b, a]

$\int_0 ^5 {9y^2 dy}$

$\int_0 ^5 \frac{9}{22} y y dy$

$\int_0 ^5 {9y dy}$

$\int_0 ^5 {18y dy}$

$\int_0^1 (e^{-y}) dy$

$\int_0^1 \frac{\sqrt{3}}{4}(e^{-y})^2 dy$

$\int_0^\infty \frac{\sqrt{3}}{4}(e^{-y})^2 dy$

$\int_0^1 \pi(e^{-y})^2 dy$

$\\pi\\int_a^b (\\sin(x))^2dx$

$\\pi\\int_a^b \\sin(x)dx$

$\\frac{\\pi}{2}\\int_a^b (\\sin(x))^3dx$

$\\pi\\int_a^b (\\cos(x))^2dx$

$0.5\pi\int_a^b( r(y))^ddddd dddddddddddddddddddddyyyyyyyyyy yy yyyyyyy yy yy yyyy yay ayay ayayya ya yayaya yayayaaa yayayaaaaaaaaaaaaaaaaaaaaaaayaaaaaaaaaaa yaaya ya ya$

$\pi\int_a^b(2r(y))dy$

$\pi\int_a^br(y)\cdot dy$

$\pi\int_a^b[r(y)]^2dy$

$\int_{0}^{1}(x-x^3)^3 dy$

$\int_{0}^{1}\frac{\sqrt{3}}{4}(x-x^6) dy$

$\int_{0}^{1}\frac{\sqrt{3}}{4}(x-x^3)^2 dy$

$\int_{0}^{1}\frac{\sqrt{3}}{4}(y-y^3)^2 dx$

$b-a$

$d=b+a$

$b=a$

$c=a-b$

Radius equals $(f(y), y)$.

Radius equals $(0,y)$.

Radius equals $f(y)$.

Radius equals $y$.

The area is $\frac{\sqrt{3}}{4}b^2$.

The area is $\sqrt{3}b^2$.

The area is $\frac{1}{2}b^2$.

The area is $\pi b^2$.