What is the integral from 1 to 2 of (1-2x^2) ?

The integral from 1 to 2 of (1-2x^2) is -11/3

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integral from 1 to 2 of (1-2x^2)

\int_{1}^{2} (1 - 2 x^{2}) d x

- \frac{11}{3}

Decimal Notation

- 3.66666 \dots

Solution steps

\int_{1}^{2} 1 - 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_{1}^{2} 1 d x - \int_{1}^{2} 2 x^{2} d x

\int_{1}^{2} 1 d x = 1

\int_{1}^{2} 2 x^{2} d x = \frac{14}{3}

= 1 - \frac{14}{3}

Simplify

1 - \frac{14}{3} : - \frac{11}{3}

= - \frac{11}{3}

\int_{0}^{π} 2 x cos (x^{2}) d x

\int_{0}^{1} e^{- x^{3}} d x

\int_{0}^{1} (2 x^{2} - 3 x) e^{x} d x

\int_{1}^{2} \frac{ln ( x )}{x ^{4}} d x

\int_{\frac{π}{3}}^{\frac{π}{2}} 3 cos^{2} (x) d x

What is the integral from 1 to 2 of (1-2x^2) ?
The integral from 1 to 2 of (1-2x^2) is -11/3