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Popular >

integral from 1 to 2 of (1-t^2)t

Solution

\int_{1}^{2} (1 - t^{2}) t d t

Solution

- \frac{9}{4}

+1

Decimal Notation

- 2.25

Solution steps

\int_{1}^{2} (1 - t^{2}) t d t

Expand

(1 - t^{2}) t : t - t^{3}

= \int_{1}^{2} t - t^{3} 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_{1}^{2} t d t - \int_{1}^{2} t^{3} d t

\int_{1}^{2} t d t = \frac{3}{2}

\int_{1}^{2} t^{3} d t = \frac{15}{4}

= \frac{3}{2} - \frac{15}{4}

Simplify

\frac{3}{2} - \frac{15}{4} : - \frac{9}{4}

= - \frac{9}{4}

Popular Examples

tangent of f(x)=4x^3+8x,(-1,-12)tangent of

f (x) = 4 x^{3} + 8 x, (- 1, - 12)

laplacetransform e^{(,\at)}laplace transform

e^{(, at)}

slope of (0,-4),(3,-7)slope

(0, - 4), (3, - 7)

inverse oflaplace (2s^3+3s^2-2s)/(s^3)inverse laplace

\frac{2 s ^{3} + 3 s ^{2} - 2 s}{s ^{3}}

derivative of m(t)=(4t+11)/(7t^2-3t+5)derivative of

m (t) = \frac{4 t + 11}{7 t ^{2} - 3 t + 5}

Frequently Asked Questions (FAQ)

What is the integral from 1 to 2 of (1-t^2)t ?
The integral from 1 to 2 of (1-t^2)t is -9/4