What is the integral from-pi/2 to-pi/3 of sec^2(3x) ?

The integral from-pi/2 to-pi/3 of sec^2(3x) is diverges

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integral from-pi/2 to-pi/3 of sec^2(3x)

\int_{- \frac{π}{2}}^{- \frac{π}{3}} sec^{2} (3 x) d x

diverges

Solution steps

\int_{- \frac{π}{2}}^{- \frac{π}{3}} sec^{2} (3 x) d x

Apply u-substitution

: \int_{- \frac{3 π}{2}}^{- π} sec^{2} (u) \frac{1}{3} d u

= \int_{- \frac{3 π}{2}}^{- π} sec^{2} (u) \frac{1}{3} d u

Take the constant out:

\int a \cdot f (x) d x = a \cdot \int f (x) d x

= \frac{1}{3} \cdot \int_{- \frac{3 π}{2}}^{- π} sec^{2} (u) d u

Use the common integral:

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

= \frac{1}{3} [tan (u)]_{- \frac{3 π}{2}}^{- π}

Compute the boundaries:

diverges

= diverges

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What is the integral from-pi/2 to-pi/3 of sec^2(3x) ?
The integral from-pi/2 to-pi/3 of sec^2(3x) is diverges