Karan L.

Mathematics Tutor since 2 years

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Trigonometry

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Question:

Find the least value of 2$$ sin^{2} $$x+3$$ cos^{2} $$x.

Karan L.

Answer:

Given, 2$$ sin^{2} $$x+3$$ cos^{2} $$x. =2$$ sin^{2} $$x+3(1-$$ sin^{2} $$x) =2$$ sin^{2} $$x+3-3$$ sin^{2} $$x =3-$$ sin^{2} $$x Thus, the least value of the above expression will occur when $$ sin^{2} $$x=1 Therefore, least value=3-1=2

Calculus

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Question:

$$ \int \mathrm{xsinx^2}\mathrm{d}x $$

Karan L.

Answer:

Let I=$$ \int \mathrm{xsinx^2}\mathrm{d}x $$ and u=$$ x^{2}$$ Thus, du=2xdx xdx=(1/2)du Now, I=1/2$$ \int \mathrm{sin u}\mathrm{d}u $$ I=1/2(-cos u)+C I=(-1/2)cos u+C Substituting u=$$ x^{2}$$, we get I=(-1/2)cos($$ x^{2}$$)+C

Algebra

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Question:

Solve for x the equation logx(8e^3) = 3

Karan L.

Answer:

Given, logx(8e^3) = 3 x^3=8e^3 x^3=(2e)^3 x=2e

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