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Questions › IIT JAM › IIT JAM 2023 › Q54
2 marksMathematics › Integration and its applications › Integration techniquesHardabout 3 min

IIT JAM 2023 Question 54: Integration and its applications

Let ∫sin⁡9xcos⁡(11x) dx=cos⁡(10x)f(x)+c\int \sin^9 x\cos(11x)\,dx=\cos(10x)f(x)+c∫sin9xcos(11x)dx=cos(10x)f(x)+c. If f′′ ⁣(π4)−k f′ ⁣(π4)=0f''\!\left(\tfrac{\pi}{4}\right)-k\,f'\!\left(\tfrac{\pi}{4}\right)=0f′′(4π​)−kf′(4π​)=0, then kkk is equal to ________ (in integer).

Answer and worked solution

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Plain-text version

Let ∫ sin⁹ xcos (11x) dx=cos (10x)f(x)+c. If f′′(π/4)-k f′(π/4)=0, then k is equal to (in integer).

Also written as: Let integral sin^9 xcos (11x) dx=cos (10x)f(x)+c. If f''(pi/4)-k f'(pi/4)=0, then k is equal to (in integer).

Integration and its applications has come up 43 times in 6 exams since 2007.

What this question tests

This question is on Integration techniques, part of Integration and its applications in Mathematics.

Substitution, integration by parts, partial fractions and improper integrals.

TestStop has 12 past-paper questions on this subtopic; the nearest in year are below.

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Question from the IIT JAM 2023 paper. Solutions are TestStop's own. Not affiliated with or endorsed by any examination authority.