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- Improper integral
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How to use it?
- Integral of d{x}:
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Integral of 1/(2+x^2)
- Integral of sin(w*t)^2
- Integral of sin(log(x))^2/x
- Integral of sin^n(x)
- Graphing y =:
- sqrt(1-(x+1)^2)
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Identical expressions
- sqrt(one -(x+ one)^ two)
- square root of (1 minus (x plus 1) squared )
- square root of (one minus (x plus one) to the power of two)
- √(1-(x+1)^2)
- sqrt(1-(x+1)2)
- sqrt1-x+12
- sqrt(1-(x+1)²)
- sqrt(1-(x+1) to the power of 2)
- sqrt1-x+1^2
- sqrt(1-(x+1)^2)dx
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Similar expressions
- sqrt(1+(x+1)^2)
- sqrt(1-(x-1)^2)
Integral of sqrt(1-(x+1)^2) dx
The solution
You have entered
[src]
-1/2 / | | ______________ | / 2 | \/ 1 - (x + 1) dx | / -1
$$\int\limits_{-1}^{- \frac{1}{2}} \sqrt{1 - \left(x + 1\right)^{2}}\, dx$$
Integral(sqrt(1 - (x + 1)^2), (x, -1, -1/2))
The answer (Indefinite)
[src]
// 3 \
|| I*acosh(1 + x) I*(1 + x) I*(1 + x) | 2| |
/ ||- -------------- + -------------------- - -------------------- for |(1 + x) | > 1|
| || 2 _______________ _______________ |
| ______________ || / 2 / 2 |
| / 2 || 2*\/ -1 + (1 + x) 2*\/ -1 + (1 + x) |
| \/ 1 - (x + 1) dx = C + |< |
| || ______________ |
/ || / 2 |
|| asin(1 + x) \/ 1 - (1 + x) *(1 + x) |
|| ----------- + ------------------------- otherwise |
|| 2 2 |
\\ /
$$\int \sqrt{1 - \left(x + 1\right)^{2}}\, dx = C + \begin{cases} \frac{i \left(x + 1\right)^{3}}{2 \sqrt{\left(x + 1\right)^{2} - 1}} - \frac{i \left(x + 1\right)}{2 \sqrt{\left(x + 1\right)^{2} - 1}} - \frac{i \operatorname{acosh}{\left(x + 1 \right)}}{2} & \text{for}\: \left|{\left(x + 1\right)^{2}}\right| > 1 \\\frac{\sqrt{1 - \left(x + 1\right)^{2}} \left(x + 1\right)}{2} + \frac{\operatorname{asin}{\left(x + 1 \right)}}{2} & \text{otherwise} \end{cases}$$
The graph
The answer
[src]
___
\/ 3 pi
- ----- - --
8 12
$$- \frac{\pi}{12} - \frac{\sqrt{3}}{8}$$
=
=
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\/ 3 pi
- ----- - --
8 12
$$- \frac{\pi}{12} - \frac{\sqrt{3}}{8}$$
-sqrt(3)/8 - pi/12
The graph
Use the examples entering the upper and lower limits of integration.