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Popular >

integral of (t^3)/3

Solution

\int \frac{t ^{3}}{3} d t

Solution

\frac{t ^{4}}{12} + C

Solution steps

\int \frac{t ^{3}}{3} d t

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int t^{3} d t

Apply the Power Rule

: \frac{t ^{4}}{4}

= \frac{1}{3} \cdot \frac{t ^{4}}{4}

Simplify

\frac{1}{3} \cdot \frac{t ^{4}}{4} : \frac{t ^{4}}{12}

= \frac{t ^{4}}{12}

Add a constant to the solution

= \frac{t ^{4}}{12} + C

Graph

Popular Examples

integral of 1/(x^2+6x-7)

\int \frac{1}{x ^{2} + 6 x - 7} d x

integral of 1/(sec(u))

\int \frac{1}{sec ( u )} d u

3y^'+(2y)/x =((y^4))/(x^4)

3 y^{^{'}} + \frac{2 y}{x} = \frac{( y ^{4} )}{x ^{4}}

tangent of 2x^3+3x^2-12x+7 tangent of

2 x^{3} + 3 x^{2} - 12 x + 7

area y=x^2,y=9,[-3,3]area

y = x^{2}, y = 9, [- 3, 3]

Frequently Asked Questions (FAQ)

What is the integral of (t^3)/3 ?
The integral of (t^3)/3 is (t^4)/(12)+C