RankLab
Back to Questions
MathsMediumNumerical2024 Β· 31 Jan Shift 2

Q88.Let 𝑦= 𝑦π‘₯ be the solution of the differential equation sec2π‘₯𝑑π‘₯+ 𝑒2𝑦tan2π‘₯+ tanπ‘₯𝑑𝑦= 0, 0 < π‘₯< πœ‹ π‘¦πœ‹ = 0. 2, 4 πœ‹ If 𝑦 = 𝛼, then 𝑒8𝛼 is equal to ______. 6

What This Question Tests

This question tests the application of definite integral properties, particularly the King's property (a to b integral of f(x) is equal to a to b integral of f(a+b-x)), along with trigonometric identities to simplify the integrand.

Concepts Tested

Definite integrationProperties of definite integrals (King's property)Trigonometric identities

Formulas Used

βˆ«β‚€α΅ƒ f(x) dx = βˆ«β‚€α΅ƒ f(a-x) dx

sin^2(x) + cos^2(x) = 1

sin(2x) = 2sin(x)cos(x)

πŸ“š NCERT Sections This Tests

2.1 β€” Two Charges 5 Γ— 10–8 C And –3 Γ— 10–8 C Are Located 16 Cm Apart. At

Physics Class 11 Β· Chapter 2

69% match

2.1 Two charges 5 Γ— 10–8 C and –3 Γ— 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.

8.17 β€” Complete Each Synthesis By Giving Missing Starting Material, Reagent Or Products

Chemistry Class 12 Β· Chapter 8

68% match

8.17 Complete each synthesis by giving missing starting material, reagent or products

2.2 β€” A Regular Hexagon Of Side 10 Cm Has A Charge 5 Mc At Each Of Its

Physics Class 11 Β· Chapter 2

68% match

2.2 A regular hexagon of side 10 cm has a charge 5 mC at each of its vertices. Calculate the potential at the centre of the hexagon.