-43 -41-1-cos x d x-2

∫^3π/4_π/41/1+cos(x)dx Compute the indefinite integral: 1/1+cos(x)dx=1/sin(x) cot(x)+C Compute the boundaries : ∫^3π/4_π/41/1+cos(x)dx=1+√(2) (√(2) 1) =1+√(2) ( ...

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Byju's Answer

Standard XII

Mathematics

Limit

∫π/43 π/41/1+...

Question

$\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{1}{1 + c o s (x)} d x = 2$

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Solution

$\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{1}{1 + c o s (x)} d x$
Compute the indefinite integral: $\frac{1}{1 + c o s (x)} d x = \frac{1}{s i n (x)} - c o t (x) + C$
Compute the boundaries : $\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{1}{1 + c o s (x)} d x = 1 + \sqrt{2} - (\sqrt{2} - 1)$
$= 1 + \sqrt{2} - (\sqrt{2} - 1)$
$= 2$ .

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Similar questions

Q. The value of

\frac{(\sqrt{2} + 1) 198}{π} \int_{π / 4}^{3 π / 4} \frac{ϕ}{1 + sin ϕ} d ϕ

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3 π / 4 \int π / 4 \frac{x}{1 + sin x} d x

is :

Q. Solve:

\frac{3 π}{4} \int \frac{π}{4} \frac{π}{1 + sin x} d x

\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{x d x}{1 + sin x} d x

Q. Evaluate

\int_{π / 4}^{3 π / 4} \frac{x sin x}{1 + sin x} d x

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∫3π4π411+cos(x)dx=2

∫3π4π411+cos(x)dx Compute the indefinite integral: 11+cos(x)dx=1sin(x)−cot(x)+C Compute the boundaries : ∫3π4π411+cos(x)dx=1+√2−(√2−1) =1+√2−(√2−1) =2.

$\int_{\frac{π}{4}}^{\frac{3 π}{4}} \frac{1}{1 + c o s (x)} d x = 2$