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Popular >

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

Solution

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

Solution

\frac{1}{3}

+1

Decimal Notation

0.33333 \dots

Solution steps

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

Expand

(2 x - 1)^{2} : 4 x^{2} - 4 x + 1

= \int_{0}^{1} 4 x^{2} - 4 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_{0}^{1} 4 x^{2} d x - \int_{0}^{1} 4 x d x + \int_{0}^{1} 1 d x

\int_{0}^{1} 4 x^{2} d x = \frac{4}{3}

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

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

= \frac{4}{3} - 2 + 1

Simplify

\frac{4}{3} - 2 + 1 : \frac{1}{3}

= \frac{1}{3}

Popular Examples

y^{''}+400y=sec(20x)

y^{^{''}} + 400 y = sec (20 x)

limit as x approaches-3+of 4x^2-7

x \to - 3 + lim (4 x^{2} - 7)

integral of e^{2x}(x^2+2x)

\int e^{2 x} (x^{2} + 2 x) d x

derivative of (t+4)^{(2/3)}(2t^2-4)^3 derivative of

(t + 4)^{(\frac{2}{3})} (2 t^{2} - 4)^{3}

limit as x approaches 2 of sqrt(x^2+12)

x \to 2 lim (x^{2} + 12)

Frequently Asked Questions (FAQ)

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