What is the antiderivative of sec-2-x- - Maths Q-A

Determine the antiderivative of sec^2(x).Now, Since d/dx(tan x)=sec^2 xso, it can be clearly seen that∫(sec^2x)dx= tan x +C Hence, the antiderivative of sec^2(x ...

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Standard XII

Mathematics

Definite Integral as Limit of Sum

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Question

What is the antiderivative of $s e c^{2} (x)$ ?

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Solution

Determine the antiderivative of $s e c^{2} (x)$ .
Now, Since $\frac{d}{d x} (\tan x) = s e c^{2} x$
so, it can be clearly seen that $\int (s e c^{2} x) d x = \tan x + C$
Hence, the antiderivative of $s e c^{2} (x)$ is $\tan x$ .

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What is the antiderivative of sec2(x)?

Determine the antiderivative of sec2(x).Now, Since ddx(tanx)=sec2xso, it can be clearly seen that∫sec2xdx=tanx+C Hence, the antiderivative of sec2(x) is tanx.

What is the antiderivative of $s e c^{2} (x)$ ?

Determine the antiderivative of $s e c^{2} (x)$ .
Now, Since $\frac{d}{d x} (\tan x) = s e c^{2} x$
so, it can be clearly seen that $\int (s e c^{2} x) d x = \tan x + C$
Hence, the antiderivative of $s e c^{2} (x)$ is $\tan x$ .