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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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Final answer to the problem

$2s-2si$
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Step-by-step Solution

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  • Integrate by partial fractions
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  • Product of Binomials with Common Term
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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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$\int_{0}^{1} s\left(1-x\right)^{-\frac{1}{2}}dx+\int_{1}^{2} s\left(1-x\right)^{-\frac{1}{2}}dx$

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Learn how to solve 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.

Final answer to the problem

$2s-2si$

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Function Plot

Plotting: $s\left(1-x\right)^{-\frac{1}{2}}$

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7
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9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
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

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