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Popular >

integral from 0 to 1 of (x^2)/(x^2+1)

Solution

\int_{0}^{1} \frac{x ^{2}}{x ^{2} + 1} d x

Solution

- \frac{π}{4} + 1

+1

Decimal Notation

0.21460 \dots

Solution steps

\int_{0}^{1} \frac{x ^{2}}{x ^{2} + 1} d x

\frac{x ^{2}}{x ^{2} + 1} = - \frac{1}{x ^{2} + 1} + 1

= \int_{0}^{1} - \frac{1}{x ^{2} + 1} + 1 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}^{1} \frac{1}{x ^{2} + 1} d x + \int_{0}^{1} 1 d x

\int_{0}^{1} \frac{1}{x ^{2} + 1} d x = \frac{π}{4}

\int_{0}^{1} 1 d x = 1

= - \frac{π}{4} + 1

Popular Examples

derivative of 1-2/x

\frac{d}{d x} (1 - \frac{2}{x})

y^{''}+xy^'-y=0

y^{^{''}} + x y^{^{'}} - y = 0

derivative of-(cos(x)/(sqrt(x)))

\frac{d}{d x} (- \frac{cos ( x )}{x})

integral of (5x^3)/(x^2-1)

\int \frac{5 x ^{3}}{x ^{2} - 1} d x

y^{''}+3y^'+2y=(1+e^t)^{-1}

y^{^{''}} + 3 y^{^{'}} + 2 y = (1 + e^{t})^{- 1}

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of (x^2)/(x^2+1) ?
The integral from 0 to 1 of (x^2)/(x^2+1) is -pi/4+1