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

The integral from 1 to 4 of (1/2 x^2+x-1) is 15

Popular >

integral from 1 to 4 of (1/2 x^2+x-1)

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

15

Solution steps

\int_{1}^{4} \frac{1}{2} x^{2} + x - 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_{1}^{4} \frac{1}{2} x^{2} d x + \int_{1}^{4} x d x - \int_{1}^{4} 1 d x

\int_{1}^{4} \frac{1}{2} x^{2} d x = \frac{21}{2}

\int_{1}^{4} x d x = \frac{15}{2}

\int_{1}^{4} 1 d x = 3

= \frac{21}{2} + \frac{15}{2} - 3

Simplify

\frac{21}{2} + \frac{15}{2} - 3 : 15

= 15

\int_{- \frac{π}{4}}^{\frac{π}{4}} sin (2 x) d x

\int_{- 3}^{- 1} (- \frac{6}{x ^{3}} - 1) d x

\int_{1}^{36} \frac{11}{x} d x

\int_{4}^{12} 1 d x

\int_{0}^{1} \frac{x ^{4}}{2 ( x ^{5} + 1 )} d x

What is the integral from 1 to 4 of (1/2 x^2+x-1) ?
The integral from 1 to 4 of (1/2 x^2+x-1) is 15