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Popular >

integral of x^3-1/2

Solution

\int x^{3} - \frac{1}{2} d x

Solution

\frac{x ^{4}}{4} - \frac{1}{2} x + C

Solution steps

\int x^{3} - \frac{1}{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 x^{3} d x - \int \frac{1}{2} d x

\int x^{3} d x = \frac{x ^{4}}{4}

\int \frac{1}{2} d x = \frac{1}{2} x

= \frac{x ^{4}}{4} - \frac{1}{2} x

Add a constant to the solution

= \frac{x ^{4}}{4} - \frac{1}{2} x + C

Graph

Popular Examples

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f (x) = - \frac{1}{( x - 5 ) ^{2}}, at x = - 3

integral of x*cos((pix)/2)

\int x \cdot cos (\frac{π x}{2}) d x

derivative of arccos(x/7)

\frac{d}{d x} (arccos (\frac{x}{7}))

derivative of (x-6/(3-4x))

\frac{d}{d x} (\frac{x - 6}{3 - 4 x})

limit as x approaches-3 of 9

x \to - 3 lim (9)

Frequently Asked Questions (FAQ)

What is the integral of x^3-1/2 ?
The integral of x^3-1/2 is (x^4)/4-1/2 x+C