Integral Calculus & Differential Equations — NDA Mathematics — Practice

Question 1

The value of ∫(5x⁴ − 3x² + 2) dx is

Accepted Answer

A

Question 2

∫ dx/(9+x²) equals

Accepted Answer

A

Question 3

∫ x² e^(x³) dx equals

Accepted Answer

A

Question 4

∫ x ln x dx equals

Accepted Answer

A

Question 5

∫ dx / [(x−1)(x+2)] equals

Accepted Answer

A

Question 6

The value of ∫₋₃³ (x⁵ − 4x³ + 2x) dx is

Accepted Answer

A

Question 7

∫₀^(π/2) [sin³x / (sin³x + cos³x)] dx equals

Accepted Answer

A

Question 8

The area bounded by y = x², the x-axis, x = 1 and x = 3 is

Accepted Answer

A

Question 9

The order and degree of the differential equation d²y/dx² = ∛(1 + dy/dx) are respectively

Accepted Answer

A

Question 10

The differential equation representing the family of curves y = Ae^(2x), where A is an arbitrary constant, is

Accepted Answer

A

Question 11

If dy/dx = 2xy and y = 3 when x = 0, then y equals

Accepted Answer

A

Question 12

A radioactive substance decays according to dN/dt = −kN. If its half-life is 20 years, the value of the decay constant k is

Accepted Answer

A

Practice — Integral Calculus & Differential Equations — NDA Mathematics