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Popular >

integral of 12-3t^2

Solution

\int 12 - 3 t^{2} d t

Solution

12 t - t^{3} + C

Solution steps

\int 12 - 3 t^{2} d t

Apply the Sum Rule:

\int f (x) \pm g (x) d x = \int f (x) d x \pm \int g (x) d x

= \int 12 d t - \int 3 t^{2} d t

\int 12 d t = 12 t

\int 3 t^{2} d t = t^{3}

= 12 t - t^{3}

Add a constant to the solution

= 12 t - t^{3} + C

Popular Examples

integral of 5t^3

\int 5 t^{3} d t

integral of (5x^2-5)/(x^3-9x^2+23x-15)

\int \frac{5 x ^{2} - 5}{x ^{3} - 9 x ^{2} + 23 x - 15} d x

integral of sin^8(3/4)x*cos^6(3/4)x

\int sin^{8} (\frac{3}{4}) x \cdot cos^{6} (\frac{3}{4}) x d x

integral of (x^3+x^2+x-5)/(x^2+2x+4)

\int \frac{x ^{3} + x ^{2} + x - 5}{x ^{2} + 2 x + 4} d x

integral of xsin(1+5x)

\int x sin (1 + 5 x) d x

Frequently Asked Questions (FAQ)

What is the integral of 12-3t^2 ?
The integral of 12-3t^2 is 12t-t^3+C