Q83.The value of the integral ∫10 xcot−1(1 −x2 + x4)dx is (1) π 4 −12 loge2 (2) π4 −loge2 (3) π 2 −loge2 (4) π2 −12 loge2
What This Question Tests
This question requires advanced manipulation of the integrand using properties of inverse trigonometric functions, followed by a suitable substitution to simplify and evaluate the definite integral.
Concepts Tested
Formulas Used
cot⁻¹(x) = tan⁻¹(1/x)
∫f(x)dx
tan⁻¹(x) - tan⁻¹(y) = tan⁻¹((x-y)/(1+xy))
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📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Properties of definite integrals
- Year
- 2019
- Shift
- 09 Apr Shift 2
- Q Number
- Q83
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
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