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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}:
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Integral of 20
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Integral of sqrt(x)*sin(x)
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Integral of cos⁵xdx
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Integral of 1/(sin^3x*cos^3x)
- Derivative of:
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sqrt(x)*sin(x)
- Graphing y =:
- sqrt(x)*sin(x)
- Limit of the function:
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sqrt(x)*sin(x)
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Identical expressions
- sqrt(x)*sin(x)
- square root of (x) multiply by sinus of (x)
- √(x)*sin(x)
- sqrt(x)sin(x)
- sqrtxsinx
- sqrt(x)*sin(x)dx
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Similar expressions
- sqrt(x)sin(x)
- sqrtxsinx/(1/3)x^2+1
- sqrt(x)*sin(x^2)
- sqrt(x)*sinx
Integral of sqrt(x)*sin(x) dx
The solution
You have entered
[src]
1 / | | ___ | \/ x *sin(x) dx | / 0
$$\int\limits_{0}^{1} \sqrt{x} \sin{\left(x \right)}\, dx$$
Integral(sqrt(x)*sin(x), (x, 0, 1))
The answer (Indefinite)
[src]
/ ___ ___\
___ ____ |\/ 2 *\/ x |
/ 5*\/ 2 *\/ pi *C|-----------|*Gamma(5/4)
| ___ | ____ |
| ___ 5*\/ x *cos(x)*Gamma(5/4) \ \/ pi /
| \/ x *sin(x) dx = C - ------------------------- + ----------------------------------------
| 4*Gamma(9/4) 8*Gamma(9/4)
/
$$\int \sqrt{x} \sin{\left(x \right)}\, dx = C - \frac{5 \sqrt{x} \cos{\left(x \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2} \sqrt{x}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
The graph
The answer
[src]
/ ___ \
___ ____ |\/ 2 |
5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
| ____|
5*cos(1)*Gamma(5/4) \\/ pi /
- ------------------- + -----------------------------------
4*Gamma(9/4) 8*Gamma(9/4)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
=
=
/ ___ \
___ ____ |\/ 2 |
5*\/ 2 *\/ pi *C|------|*Gamma(5/4)
| ____|
5*cos(1)*Gamma(5/4) \\/ pi /
- ------------------- + -----------------------------------
4*Gamma(9/4) 8*Gamma(9/4)
$$- \frac{5 \cos{\left(1 \right)} \Gamma\left(\frac{5}{4}\right)}{4 \Gamma\left(\frac{9}{4}\right)} + \frac{5 \sqrt{2} \sqrt{\pi} C\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{5}{4}\right)}{8 \Gamma\left(\frac{9}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.