What is the integral from-1 to 2 of tsin(t^2)+2t^3 ?

The integral from-1 to 2 of tsin(t^2)+2t^3 is 1/2 (-cos(4)+cos(1))+15/2

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integral from-1 to 2 of tsin(t^2)+2t^3

\int_{- 1}^{2} t sin (t^{2}) + 2 t^{3} d t

\frac{1}{2} (- cos (4) + cos (1)) + \frac{15}{2}

Decimal Notation

8.09697 \dots

Solution steps

\int_{- 1}^{2} t sin (t^{2}) + 2 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 sin (t^{2}) d t + \int_{- 1}^{2} 2 t^{3} d t

\int_{- 1}^{2} t sin (t^{2}) d t = \frac{1}{2} (- cos (4) + cos (1))

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

= \frac{1}{2} (- cos (4) + cos (1)) + \frac{15}{2}

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What is the integral from-1 to 2 of tsin(t^2)+2t^3 ?
The integral from-1 to 2 of tsin(t^2)+2t^3 is 1/2 (-cos(4)+cos(1))+15/2