What is the integral from 0 to tan(θ) of sec^2(y) ?

The integral from 0 to tan(θ) of sec^2(y) is tan(tan(θ))

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integral from 0 to tan(θ) of sec^2(y)

\int_{0}^{t a n (θ)} sec^{2} (y) d y

tan (tan (θ))

Solution steps

\int_{0}^{t a n (θ)} sec^{2} (y) d y

Use the common integral:

\int sec^{2} (y) d y = tan (y)

= [tan (y)]_{0}^{t a n (θ)}

Compute the boundaries:

tan (tan (θ))

= tan (tan (θ))

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What is the integral from 0 to tan(θ) of sec^2(y) ?
The integral from 0 to tan(θ) of sec^2(y) is tan(tan(θ))