Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \sin x \cos x d x$ Solution:...
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Question: Evaluate the following integrals: $\int \operatorname{cosec}^{2}(2 x+5) d x$ Solution: Formula $\int \operatorname{cosec}^{2} x d x=-\cot x+c$...
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Question: Evaluate the following integrals: $\int \sin x \sqrt{1+\cos 2 x} d x$ Solution:...
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Question: Evaluate the following integrals: $\int \cos (5+6 x) d x$ Solution:...
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Question: Evaluate the following integrals: $\int \sin 3 x d x$ Solution: Formula $=\int \sin x d x=-\cos x+c$...
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Question: Evaluate the following integrals: $\int 3^{(2-3 x)} d x$ Solution:...
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Question: Evaluate the following integrals: $\int e^{(1-3 x)} d x$ Solution:...
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Question: Evaluate the following integrals: $\int e^{(2 x-1)} d x$ Solution:...
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Question: Evaluate the following integrals: $\int \frac{1}{(2 x-3)^{3 / 2}} d x$ Solution:...
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Question: Evaluate the following integrals: $\int \frac{1}{\sqrt{3-4 x}} d x$ Solution:...
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Question: Evaluate the following integrals: $\int \frac{1}{\sqrt{4 x+3}} d x$ Solution:...
Read More →A mass of 6 × 1024 kg (equal to the mass of the earth)
Question: A mass of $6 \times 1024 \mathrm{~kg}$ (equal to the mass of the earth) is to be compressed in a sphere in such a way that the escape velocity from its surface is $3 \times 108 \mathrm{~m} / \mathrm{s}$. What should be the radius of the sphere? Solution:...
Read More →A particle is fired vertically upward with a speed of
Question: A particle is fired vertically upward with a speed of $15 \mathrm{~km} / \mathrm{s}$. With what speed will it move in Interstellar space. Assume only earth's gravitational field. Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: $\int \sqrt{3 x-5} d x$ Solution:...
Read More →A particle is fired vertically upward from earth's surface and
Question: A particle is fired vertically upward from earth's surface and it goes up to a maximum height of $6400 \mathrm{~km}$. Find the initial speed of the particle. Solution:...
Read More →Evaluate the following integrals:
Question: Evaluate the following integrals: Solution:...
Read More →Find the minimum colatitude
Question: Find the minimum colatitude which can directly receive a signal from a geostationary satellite. Solution:...
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Question: Evaluate the following integrals: $\int(2 x+9)^{5} d x$ Solution:...
Read More →The radius of a planet is R,
Question: The radius of a planet is $\mathrm{R}$, and a satellite revolves round it in a circle of radius $\mathrm{R} 2$. The time period of revolution is $\mathrm{T}$. Find the acceleration due to the gravitation of the planet at its surface. Solution:...
Read More →What is the true weight of an object in a geostationary satellite
Question: What is the true weight of an object in a geostationary satellite that weighed exactly $10^{\prime} 0 \mathrm{~N}$ at the north pole? Solution:...
Read More →(a) Find the radius of the circular orbit of a satellite moving with
Question: (a) Find the radius of the circular orbit of a satellite moving with an angular speed equal to the angular speed of earth's rotation. (b) If the satellite is directly above the north pole at some instant, find the time it takes to come over the equatorial plane. Mass of the earth $=6 \times 10^{24} \mathrm{~kg}$. Solution:...
Read More →A satellite of mass 1000 kg is supposed to orbit the earth at a height of 2000 km
Question: A satellite of mass $1000 \mathrm{~kg}$ is supposed to orbit the earth at a height of $2000 \mathrm{~km}$ above the earth's surface. Find (a) its speed in the orbit, (b) its kinetic energy, (c) the potential energy of the earth-satellite system and (d) its time period. Mass of the earth $=6 \times 1024 \mathrm{~kg}$. Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cos 4 x \cos x d x=?$ A. $\frac{1}{5} \sin 5 x+\frac{1}{3} \sin 3 x+C$ B. $\frac{1}{5} \cos 5 x-\frac{1}{3} \cos 3 x+C$ C. $\frac{1}{10} \sin 5 x+\frac{1}{6} \sin 3 x+C$ D. None of these Solution:...
Read More →Mark against the correct answer in each of the following:
Question: Mark $(\sqrt{)}$ against the correct answer in each of the following: $\int \cos 3 x \sin 2 x d x=?$ A. $\frac{1}{2} \cos x-\frac{1}{10} \cos 5 x+C$ B. $-\frac{1}{2} \sin x+\frac{1}{10} \sin 5 x+C$ C. $-\frac{1}{2} \cos x+\frac{1}{10} \cos 5 x+C$ D. None of these Solution:...
Read More →Solve this following
Question: Mark $(\sqrt{ })$ against the correct answer in each of the following: $\int \sin 3 x \sin 2 x d x=?$ A. $-\frac{1}{5} \cos 5 x+C$ B. $\frac{1}{2} \sin x+\frac{1}{10} \sin 5 x-C$ C. $\frac{1}{2} \sin x-\frac{1}{10} \sin 5 x-C$ D. $-\frac{1}{3} \cos 3 x-\frac{1}{2} \sin 2 x+C$ Solution:...
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