Q76.The area (in square units) of the region enclosed by the ellipse x2 + 3y2 = 18 in the first quadrant below the line y = x is (1) √3π −34 (2) √3π + 1 (3) √3π (4) √3π + 34
What This Question Tests
This question primarily tests the application of integration by parts for a specific type of integrand involving the inverse hyperbolic sine function (or its equivalent logarithmic form).
Concepts Tested
Formulas Used
∫ u dv = uv - ∫ v du
∫ log(x + √(x²+a²)) dx = x log(x + √(x²+a²)) - √(x²+a²)
📚 NCERT Sections This Tests
2.4 — A Spherical Conductor Of Radius 12 Cm Has A Charge Of 1.6 × 10–7C
Physics Class 11 · Chapter 2
2.4 A spherical conductor of radius 12 cm has a charge of 1.6 × 10–7C distributed uniformly on its surface. What is the electric field (a) inside the sphere (b) just outside the sphere (c) at a point 18 cm from the centre of the sphere?
1.18 — A Point Charge Of 2.0 Mc Is At The Centre Of A Cubic Gaussian
Physics Class 11 · Chapter 1
1.18 A point charge of 2.0 mC is at the centre of a cubic Gaussian surface 9.0 cm on edge. What is the net electric flux through the surface?
2.1 — Two Charges 5 × 10–8 C And –3 × 10–8 C Are Located 16 Cm Apart. At
Physics Class 11 · Chapter 2
2.1 Two charges 5 × 10–8 C and –3 × 10–8 C are located 16 cm apart. At what point(s) on the line joining the two charges is the electric potential zero? Take the potential at infinity to be zero.
📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Integration by parts for inverse hyperbolic functions
- Year
- 2024
- Shift
- 09 Apr Shift 2
- Q Number
- Q76
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
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