Evaluate ∫cos2 xdx_________
Evaluate ∫cos2 xdx_________
-x/2+sin2x/4+c
x/2+sin2x/2+c
x/2+sin2x/4+c
-x/2+cos4x/4+c626d12d417cb86275feefcba
The Correct Option is A
Solution and Explanation
The correct option is (A): -x/2+sin2x/4+c
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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:
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