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Popular >

integral from 1 to 5 of 2+3x-x^2

Solution

\int_{1}^{5} 2 + 3 x - x^{2} d x

Solution

\frac{8}{3}

+1

Decimal Notation

2.66666 \dots

Solution steps

\int_{1}^{5} 2 + 3 x - 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}^{5} 2 d x + \int_{1}^{5} 3 x d x - \int_{1}^{5} x^{2} d x

\int_{1}^{5} 2 d x = 8

\int_{1}^{5} 3 x d x = 36

\int_{1}^{5} x^{2} d x = \frac{124}{3}

= 8 + 36 - \frac{124}{3}

Simplify

8 + 36 - \frac{124}{3} : \frac{8}{3}

= \frac{8}{3}

Popular Examples

derivative of (x^2-11x+10/(x^2+11x+10))

\frac{d}{d x} (\frac{x ^{2} - 11 x + 10}{x ^{2} + 11 x + 10})

derivative of (x^2-2/(5x^3+6))

\frac{d}{d x} (\frac{x ^{2} - 2}{5 x ^{3} + 6})

(\partial)/(\partial x)(sqrt(a^2-x^2))

\frac{\partial}{\partial x} (a^{2} - x^{2})

integral of (arcsin(x))/(sqrt(1-x))

\int \frac{arcsin ( x )}{1 - x} d x

f(x)=ln(ln(3x))

f (x) = ln (ln (3 x))

Frequently Asked Questions (FAQ)

What is the integral from 1 to 5 of 2+3x-x^2 ?
The integral from 1 to 5 of 2+3x-x^2 is 8/3