Q74.If ∫100π0 sin2x xx dx = 1+4π2απ3 π −[ π ]) e ( α is: (1) 200(1 −e−1) (2) 100(1 −e) (3) 50(e −1) (4) 150(e−1 −1)
What This Question Tests
This question requires careful manipulation of a definite integral using properties of integration and potentially advanced techniques or substitution to simplify and evaluate it.
Concepts Tested
Formulas Used
∫(0 to na) f(x)dx = n∫(0 to a) f(x)dx if f(x+a) = f(x)
By parts integration
Integral of x^(n-1) e^(-x) dx from 0 to infinity = Gamma(n)
📚 NCERT Sections This Tests
12.5 — A Hydrogen Atom Initially In The Ground Level Absorbs A Photon,
Physics Class 12 · Chapter 12
12.5 A hydrogen atom initially in the ground level absorbs a photon, which excites it to the n = 4 level. Determine the wavelength and frequency of photon.
12.1 — (A) No Different From
Physics Class 12 · Chapter 12
12.1 (a) No different from (b) Thomson’s model; Rutherford’s model (c) Rutherford’s model (d) Thomson’s model; Rutherford’s model (e) Both the models
14.2 — Which Of The Statements Given In Exercise 14.1 Is True For P-Type
Physics Class 12 · Chapter 14
14.2 Which of the statements given in Exercise 14.1 is true for p-type semiconductos.
📋 Question Details
- Chapter
- Definite Integration & Area
- Topic
- Definite integrals, Properties of definite integrals
- Year
- 2021
- Shift
- 22 Jul Shift 1
- Q Number
- Q74
- Type
- MCQ
- NCERT Ref
- Class 12 Mathematics Ch 7: Integrals
More from this Chapter
Q96.Let I = ∫10 sin√xx dx and J = ∫10 cos√xx (1) I > 32 and J > 2 (2) I < 23 and J < 2 (3) I < 32 and J > 2 (4) I > 23 and J < 2
Q97.The area of the plane region bounded by the curves x + 2y2 = 0 and x + 3y2 = 1 is equal to (1) 5 (2) 1 3 3 (3) 2 (4) 4 3 3
Q84.The area of the region bounded by the parabola (y −2)2 = x −1, the tangent to the parabola at the point (2, 3) and the x-axis is (1) 3 (2) 6 (3) 9 (4) 12 JEE Main 2009 JEE Main Previous Year Paper
Q85.The differential equation which represents the family of curves y = c1ec2x , where c1 and c2 are arbitrary constants is (1) y′ = y2 (2) y′′ = y′y (3) yy′′ = y′ (4) yy′′ = (y′)2