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Popular >

integral from 0 to 1 of-x^2+4x+1

Solution

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

Solution

\frac{8}{3}

+1

Decimal Notation

2.66666 \dots

Solution steps

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

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

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

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

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

Simplify

- \frac{1}{3} + 2 + 1 : \frac{8}{3}

= \frac{8}{3}

Popular Examples

integral of 1/(7x+4)

\int \frac{1}{7 x + 4} d x

implicit (dy)/(dx),xy-6=0 implicit derivative

\frac{d y}{d x}, x y - 6 = 0

integral of 2sin^3(5x)cos^3(5x)

\int 2 sin^{3} (5 x) cos^{3} (5 x) d x

derivative of \sqrt[3]{x^2+1}

(\partial)/(\partial x)(sin^3(x^2y))

\frac{\partial}{\partial x} (sin^{3} (x^{2} y))

Frequently Asked Questions (FAQ)

What is the integral from 0 to 1 of-x^2+4x+1 ?
The integral from 0 to 1 of-x^2+4x+1 is 8/3