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Popular >

integral from 0 to 2 of 2-x^2

Solution

\int_{0}^{2} 2 - x^{2} d x

Solution

\frac{4}{3}

+1

Solution steps

\int_{0}^{2} 2 - x^{2} d x

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int_{0}^{2} 2 d x - \int_{0}^{2} x^{2} d x

\int_{0}^{2} 2 d x = 4

\int_{0}^{2} x^{2} d x = \frac{8}{3}

= 4 - \frac{8}{3}

Simplify

4 - \frac{8}{3} : \frac{4}{3}

= \frac{4}{3}

Popular Examples

ty^'+2y=sin(t),y(pi/2)=1

t y^{^{'}} + 2 y = sin (t), y (\frac{π}{2}) = 1

f(x)= 1/(x^{2/3)}

f (x) = \frac{1}{x ^{\frac{2}{3}}}

integral of (4x^3+3x+3)/x

\int \frac{4 x ^{3} + 3 x + 3}{x} d x

limit as x approaches 7 of sin(pi/x)

x \to 7 lim (sin (\frac{π}{x}))

(\partial)/(\partial y)(y/(x-1))

\frac{\partial}{\partial y} (\frac{y}{x - 1})

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of 2-x^2 ?
The integral from 0 to 2 of 2-x^2 is 4/3