Evaluate
4\pi t\cos(t)
Differentiate w.r.t. t
4\pi \left(-t\sin(t)+\cos(t)\right)
Share
Copied to clipboard
\int 2t\cos(t)\mathrm{d}x
Evaluate the indefinite integral first.
2t\cos(t)x
Find the integral of 2t\cos(t) using the table of common integrals rule \int a\mathrm{d}x=ax.
2\times 2t\cos(t)\pi +0\times 2t\cos(t)
The definite integral is the antiderivative of the expression evaluated at the upper limit of integration minus the antiderivative evaluated at the lower limit of integration.
4\cos(t)t\pi
Simplify.
Examples
Quadratic equation
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometry
4 \sin \theta \cos \theta = 2 \sin \theta
Linear equation
y = 3x + 4
Arithmetic
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Simultaneous equation
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiation
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Limits
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}