Mister Exam
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- Improper integral
- Double Integral
- Triple Integral
- Curvilinear integral
- Derivative Step by Step
- Differential equations Step by Step
- Limits Step by Step
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How to use it?
- Integral of d{x}:
- Integral of (x^2)*(cos(nx))
- Integral of cos(nx)
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Integral of xdy
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Integral of arcsin(x)+arccos(x)
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Identical expressions
- (x^ two)*(cos(nx))
- (x squared ) multiply by ( co sinus of e of (nx))
- (x to the power of two) multiply by ( co sinus of e of (nx))
- (x2)*(cos(nx))
- x2*cosnx
- (x²)*(cos(nx))
- (x to the power of 2)*(cos(nx))
- (x^2)(cos(nx))
- (x2)(cos(nx))
- x2cosnx
- x^2cosnx
- (x^2)*(cos(nx))dx
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Similar expressions
- x^2cosnx
- (pi^2-x^2)*cos(n*x)
- x^2cos(nx)
Integral of (x^2)*(cos(nx)) dx
The solution
You have entered
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1 / | | 2 | x *cos(n*x) dx | / 0
$$\int\limits_{0}^{1} x^{2} \cos{\left(n x \right)}\, dx$$
The answer (Indefinite)
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// 3 \
|| x |
|| -- for n = 0|
|| 3 |
/ || |
| ||/sin(n*x) x*cos(n*x) | // x for n = 0\
| 2 |||-------- - ---------- for n != 0 | 2 || |
| x *cos(n*x) dx = C - 2*|<| 2 n | + x *|
$${{\left(n^2\,x^2-2\right)\,\sin \left(n\,x\right)+2\,n\,x\,\cos
\left(n\,x\right)}\over{n^3}}$$
The answer
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/sin(n) 2*sin(n) 2*cos(n) |------ - -------- + -------- for And(n > -oo, n < oo, n != 0) | n 3 2 < n n | | 1/3 otherwise \
$${{\left(n^2-2\right)\,\sin n+2\,n\,\cos n}\over{n^3}}$$
=
=
/sin(n) 2*sin(n) 2*cos(n) |------ - -------- + -------- for And(n > -oo, n < oo, n != 0) | n 3 2 < n n | | 1/3 otherwise \
$$\begin{cases} \frac{\sin{\left(n \right)}}{n} + \frac{2 \cos{\left(n \right)}}{n^{2}} - \frac{2 \sin{\left(n \right)}}{n^{3}} & \text{for}\: n > -\infty \wedge n < \infty \wedge n \neq 0 \\\frac{1}{3} & \text{otherwise} \end{cases}$$
Use the examples entering the upper and lower limits of integration.