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- Improper integral
- Double Integral
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- Curvilinear integral
- Derivative Step by Step
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How to use it?
- Integral of d{x}:
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Integral of 4*x/(1+x^2)
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Integral of x/(x^3-8)
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Integral of x/sqrt(1+x)
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Integral of (1-2*x)*exp(-2*x)
- Graphing y =:
- sqrt(4-x^2)/x
- Derivative of:
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sqrt(4-x^2)/x
- Limit of the function:
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sqrt(4-x^2)/x
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Identical expressions
- sqrt(four -x^ two)/x
- square root of (4 minus x squared ) divide by x
- square root of (four minus x to the power of two) divide by x
- √(4-x^2)/x
- sqrt(4-x2)/x
- sqrt4-x2/x
- sqrt(4-x²)/x
- sqrt(4-x to the power of 2)/x
- sqrt4-x^2/x
- sqrt(4-x^2) divide by x
- sqrt(4-x^2)/xdx
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Similar expressions
- sqrt(4+x^2)/x
Integral of sqrt(4-x^2)/x dx
The solution
You have entered
[src]
1 / | | ________ | / 2 | \/ 4 - x | ----------- dx | x | / 0
$$\int\limits_{0}^{1} \frac{\sqrt{4 - x^{2}}}{x}\, dx$$
Integral(sqrt(4 - x^2)/x, (x, 0, 1))
The answer (Indefinite)
[src]
// /2\ x 4 4 \
||- 2*acosh|-| - -------------- + ---------------- for ---- > 1|
/ || \x/ _________ _________ | 2| |
| || / 4 / 4 |x | |
| ________ || / -1 + -- x* / -1 + -- |
| / 2 || / 2 / 2 |
| \/ 4 - x || \/ x \/ x |
| ----------- dx = C + |< |
| x || /2\ I*x 4*I |
| || 2*I*asin|-| + ------------- - --------------- otherwise |
/ || \x/ ________ ________ |
|| / 4 / 4 |
|| / 1 - -- x* / 1 - -- |
|| / 2 / 2 |
\\ \/ x \/ x /
$$\int \frac{\sqrt{4 - x^{2}}}{x}\, dx = C + \begin{cases} - \frac{x}{\sqrt{-1 + \frac{4}{x^{2}}}} - 2 \operatorname{acosh}{\left(\frac{2}{x} \right)} + \frac{4}{x \sqrt{-1 + \frac{4}{x^{2}}}} & \text{for}\: \frac{4}{\left|{x^{2}}\right|} > 1 \\\frac{i x}{\sqrt{1 - \frac{4}{x^{2}}}} + 2 i \operatorname{asin}{\left(\frac{2}{x} \right)} - \frac{4 i}{x \sqrt{1 - \frac{4}{x^{2}}}} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
oo - 2*acosh(2)
$$- 2 \operatorname{acosh}{\left(2 \right)} + \infty$$
=
=
oo - 2*acosh(2)
$$- 2 \operatorname{acosh}{\left(2 \right)} + \infty$$
oo - 2*acosh(2)
The graph
Use the examples entering the upper and lower limits of integration.