Question:
If I =$ \int sec ^4x \, cosec ^2x \,dx$ =K tan ^3x +L tan x+M cot x + const, then
If I =$ \int sec ^4x \, cosec ^2x \,dx$ =K tan ^3x +L tan x+M cot x + const, then
Updated On: Apr 17, 2024
- $K= \frac {1}{3}$L = 1,M = 2
- $K= \frac {1}{3}$L = 2,M = -1
- K = - 1, L = 0, M = 1
- none of these
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The Correct Option is B
Solution and Explanation
Answer (b) $K= \frac {1}{3}$L = 2,M = -1
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Concepts Used:
Integration by Parts
Integration by Parts is a mode of integrating 2 functions, when they multiplied with each other. For two functions ‘u’ and ‘v’, the formula is as follows:
∫u v dx = u∫v dx −∫u' (∫v dx) dx
- u is the first function u(x)
- v is the second function v(x)
- u' is the derivative of the function u(x)
The first function ‘u’ is used in the following order (ILATE):
- 'I' : Inverse Trigonometric Functions
- ‘L’ : Logarithmic Functions
- ‘A’ : Algebraic Functions
- ‘T’ : Trigonometric Functions
- ‘E’ : Exponential Functions
The rule as a diagram:
