What is the integral from 0 to x of t^2cos(t) ?

The integral from 0 to x of t^2cos(t) is x^2sin(x)-2(sin(x)-xcos(x))

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integral from 0 to x of t^2cos(t)

\int_{0}^{x} t^{2} cos (t) d t

x^{2} sin (x) - 2 (sin (x) - x cos (x))

Solution steps

\int_{0}^{x} t^{2} cos (t) d t

Apply Integration By Parts

: [t^{2} sin (t) - \int 2 t sin (t) d t]_{0}^{x}

= [t^{2} sin (t) - \int 2 t sin (t) d t]_{0}^{x}

\int 2 t sin (t) d t = 2 (- t cos (t) + sin (t))

= [t^{2} sin (t) - 2 (- t cos (t) + sin (t))]_{0}^{x}

Compute the boundaries:

x^{2} sin (x) - 2 (sin (x) - x cos (x))

= x^{2} sin (x) - 2 (sin (x) - x cos (x))

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

(2 x - x) (5 x + 2)

f (x) = x^{3} - 2 x + 1, (2, 5)

\frac{d}{d t} (3 t)

16 ln (x^{2}) - x^{2}

What is the integral from 0 to x of t^2cos(t) ?
The integral from 0 to x of t^2cos(t) is x^2sin(x)-2(sin(x)-xcos(x))