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Integrate the function $\frac{1}{1-\sin\left(o\right)}$ from 0 to $1$

Step-by-step Solution

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Solving: $\int_{0}^{1}\frac{1}{1-\sin\left(o\right)}do$
Solve instead: $\int_{0}^{1}\frac{1}{1-\sin\left(o\right)}dx$

Solution

Formulas

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Final Answer

$2.408219$
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Step-by-step Solution

Problem to solve:

$\int_{0}^{1}\frac{1}{1-\sin\left(o\right)}do$

Specify the solving method

1

We can solve the integral $\int\frac{1}{1-\sin\left(o\right)}do$ by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of $t$ by setting the substitution

$t=\tan\left(\frac{o}{2}\right)$

Learn how to solve definite integrals problems step by step online.

$t=\tan\left(\frac{o}{2}\right)$

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Learn how to solve definite integrals problems step by step online. Integrate the function 1/(1-sin(o)) from 0 to 1. We can solve the integral \int\frac{1}{1-\sin\left(o\right)}do by applying the method Weierstrass substitution (also known as tangent half-angle substitution) which converts an integral of trigonometric functions into a rational function of t by setting the substitution. Hence. Substituting in the original integral we get. Simplifying.

Final Answer

$2.408219$

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(1/(1-sin(o)))do&0&1 using basic integralsSolve int(1/(1-sin(o)))do&0&1 using u-substitutionSolve int(1/(1-sin(o)))do&0&1 using integration by partsSolve int(1/(1-sin(o)))do&0&1 using tabular integrationSolve int(1/(1-sin(o)))do&0&1 using weierstrass substitution

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0
a
b
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d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
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

How to improve your answer:

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Main topic:

Definite Integrals

Used formulas:

4. See formulas

Time to solve it:

~ 0.11 s

Related topics:

Definite IntegralsIntegral CalculusCalculusFactorizationWeierstrass SubstitutionIntegration TechniquesIntegrals of Rational Functions of Sine and CosinePerfect Square TrinomialIntegration by SubstitutionIntegrals of Polynomial Functions

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