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Popular >

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

Solution

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

Solution

\frac{22}{3}

+1

Decimal Notation

7.33333 \dots

Solution steps

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

\int_{0}^{2} 2 x^{2} d x = \frac{16}{3}

\int_{0}^{2} 1 d x = 2

= \frac{16}{3} + 2

Simplify

\frac{16}{3} + 2 : \frac{22}{3}

= \frac{22}{3}

Popular Examples

integral of e^{x+2}

\int e^{x + 2} d x

(\partial)/(\partial m)(mx^b)

\frac{\partial}{\partial m} (m x^{b})

derivative of sqrt(x-x^2)

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

(\partial)/(\partial x)(e^{3x^2y}(1+x-2y))

\frac{\partial}{\partial x} (e^{3 x^{2} y} (1 + x - 2 y))

derivative of sqrt(9-4x)

\frac{d}{d x} (9 - 4 x)

Frequently Asked Questions (FAQ)

What is the integral from 0 to 2 of (2x^2+1) ?
The integral from 0 to 2 of (2x^2+1) is 22/3