Definite Integrals
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Solve the integral I=∫R∞GMmx2dx
- GMm ln(R)
The velocity v and displacement x of a particle executing simple harmonic motion are related as
vdvdx=−ω2x
At x=0, v=v0. Find the velocity v when the displacement becomes x.
None of these
∫π/2−π/2cos xdx
None of these
1 unit
2 units
0 unit
You are given a rod of length 'L'. The linear mass density varies as λ′. λ=a+bx. Here a & b are constants and the mass of the rod increases as x increases. Find the mass of the rod.
None of these
Solve the integral I = ∫π0sin2xdx
0
∫100sec2(3x+6)dx
None of these
Where should the tank be punctured so that water coming out has maximum horizontal range?
None of these
y=h2
y=h4
y=h3
Find the area enclosed by the curve y=x2 and the x-axis for interval x = 1 to x = 3.
9 sq. units
27.2 sq. units
10 sq. units
263 sq. units
- 43[√2−1]
- 2√2−2
- 43[√2−1]
- 23[2√2−1]