∫ 0 π /4 ( c o s 3 x + s i n 3 x ) 2 c o s 2 x s i n 2 x d x is equal to

Divide Nr & Dr by cos x ∫ 0 π /4 ( 1 + t a n 3 x ) 2 t a n 2 x s e c 2 x d x d x Let 1 + tan 3 x = t tan 2 x sec 2 x d x = 3 d t 3 1 ∫ 1 2 t 2 dt = 6 1

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Mathematics - Definite Integration Question with Solution | TestHub

MathematicsDefinite IntegrationDefinite Integration by SubstitutionHard2 minPYQ_2024

MathematicsHardsingle choice

$\int_{0}^{π /4} \frac{c o s ^{2} x s i n ^{2} x}{( c o s ^{3} x + s i n ^{3} x ) ^{2}} d x$ is equal to

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Answer:

Solution:

Divide $Nr & Dr$ by $cos x$ $\int_{0}^{π /4} \frac{t a n ^{2} x s e c ^{2} x d x}{( 1 + t a n ^{3} x ) ^{2}} d x$
Let $1 + tan^{3} x = t$ $tan^{2} x sec^{2} x d x = \frac{d t}{3} \frac{1}{3} \int_{1}^{2} \frac{dt}{t ^{2}} = \frac{1}{6}$

Stream:JEESubject:MathematicsTopic:Definite IntegrationSubtopic:Definite Integration by Substitution

⏱ 2mℹ️ Source: PYQ_2024

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