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 sqrt(x)*cos(x)
- Integral of (x^2-y^2)
-
Integral of cost^2
- Integral of sin(log2(x))/x
- Graphing y =:
- sqrt(x)*cos(x)
- Sum of series:
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sqrt(x)*cos(x)
- Derivative of:
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sqrt(x)*cos(x)
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Identical expressions
- sqrt(x)*cos(x)
- square root of (x) multiply by co sinus of e of (x)
- √(x)*cos(x)
- sqrt(x)cos(x)
- sqrtxcosx
- sqrt(x)*cos(x)dx
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Similar expressions
- (sqrt(x)cos(x))/(x+100)
- ((sqrtx)cosx)/(x+10)
- sqrt(x)*cosx
Integral of sqrt(x)*cos(x) dx
The solution
You have entered
[src]
1 / | | ___ | \/ x *cos(x) dx | / 0
$$\int\limits_{0}^{1} \sqrt{x} \cos{\left(x \right)}\, dx$$
The answer (Indefinite)
[src]
/ ___ ___\
___ ____ |\/ 2 *\/ x |
/ 3*\/ 2 *\/ pi *S|-----------|*Gamma(3/4)
| ___ | ____ |
| ___ 3*\/ x *Gamma(3/4)*sin(x) \ \/ pi /
| \/ x *cos(x) dx = C + ------------------------- - ----------------------------------------
| 4*Gamma(7/4) 8*Gamma(7/4)
/
$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left({{\left(\sqrt{2}\,i+\sqrt{2}\right)\,\sqrt{x}
}\over{2}}\right)+\left(\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}
\left({{\left(\sqrt{2}\,i-\sqrt{2}\right)\,\sqrt{x}}\over{2}}\right)
+\left(\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}\left(\sqrt{-i}\,
\sqrt{x}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,\mathrm{erf}
\left(\left(-1\right)^{{{1}\over{4}}}\,\sqrt{x}\right)\right)-16\,
\sqrt{x}\,\sin x}\over{16}}$$
The graph
The answer
[src]
/ ___ \
___ ____ |\/ 2 |
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
| ____|
3*Gamma(3/4)*sin(1) \\/ pi /
------------------- - -----------------------------------
4*Gamma(7/4) 8*Gamma(7/4)
$$-{{\sqrt{\pi}\,\left(\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left({{\sqrt{2}\,i+\sqrt{2}}\over{2}}\right)+\left(
\sqrt{2}\,i-\sqrt{2}\right)\,\mathrm{erf}\left({{\sqrt{2}\,i-\sqrt{2
}}\over{2}}\right)+\left(\sqrt{2}-\sqrt{2}\,i\right)\,\mathrm{erf}
\left(\sqrt{-i}\right)+\left(\sqrt{2}\,i+\sqrt{2}\right)\,
\mathrm{erf}\left(\left(-1\right)^{{{1}\over{4}}}\right)\right)-16\,
\sin 1}\over{16}}$$
=
=
/ ___ \
___ ____ |\/ 2 |
3*\/ 2 *\/ pi *S|------|*Gamma(3/4)
| ____|
3*Gamma(3/4)*sin(1) \\/ pi /
------------------- - -----------------------------------
4*Gamma(7/4) 8*Gamma(7/4)
$$- \frac{3 \sqrt{2} \sqrt{\pi} S\left(\frac{\sqrt{2}}{\sqrt{\pi}}\right) \Gamma\left(\frac{3}{4}\right)}{8 \Gamma\left(\frac{7}{4}\right)} + \frac{3 \sin{\left(1 \right)} \Gamma\left(\frac{3}{4}\right)}{4 \Gamma\left(\frac{7}{4}\right)}$$
The graph
Use the examples entering the upper and lower limits of integration.