Question:
If \(\frac{d y}{d x}+2 y \tan x=\sin x, 0\)
If \(\frac{d y}{d x}+2 y \tan x=\sin x, 0\)
Updated On: Dec 20, 2023
- $\frac{1}{8}$
- $\frac{3}{4}$
- $\frac{1}{4}$
- $\frac{3}{8}$
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The Correct Option is A
Solution and Explanation
The correct option is(A): \(\frac{1}{8}\).
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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:
