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# Integrate the function $s\left(1-x\right)^{-\frac{1}{2}}$ from 0 to $2$

## Step-by-step Solution

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###  Videos

$2s-2\sqrt{-1}s$
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##  Step-by-step Solution 

Problem to solve:

$\int_{0}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$

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Since the integral $\int_{0}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$ has a discontinuity inside the interval, we have to split it in two integrals

$\int_{0}^{1} s\left(1-x\right)^{-\frac{1}{2}}dx+\int_{1}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$

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$\int_{0}^{1} s\left(1-x\right)^{-\frac{1}{2}}dx+\int_{1}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$

Learn how to solve integral calculus problems step by step online. Integrate the function s(1-x)^(-1/2) from 0 to 2. Since the integral \int_{0}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx has a discontinuity inside the interval, we have to split it in two integrals. The integral \int_{0}^{1} s\left(1-x\right)^{-\frac{1}{2}}dx results in: 2s. The integral \int_{1}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx results in: -2\sqrt{-1}s. Gather the results of all integrals.

$2s-2\sqrt{-1}s$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

Solve int(s(1-x)^(-1/2))dx&0&2 using partial fractionsSolve int(s(1-x)^(-1/2))dx&0&2 using basic integralsSolve int(s(1-x)^(-1/2))dx&0&2 using u-substitutionSolve int(s(1-x)^(-1/2))dx&0&2 using integration by partsSolve int(s(1-x)^(-1/2))dx&0&2 using trigonometric substitution

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a
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x
y
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+
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◻/◻
/
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2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

### Main topic:

Integral Calculus

~ 0.13 s

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