To solve the integral ∫23tan2θsecθdθ, we can use a trigonometric identity to simplify the integrand. We know that tan2θ=sec2θ−1, so we can rewrite the integrand in terms of secθ and simplify. After simplification, we can integrate the resulting expression over the given limits.
Step 1: Set Up the Integral
We start with the integral
I=∫23tan2θsecθdθ.
Step 2: Simplify the Integrand
Using the identity tan2θ=sec2θ−1, we can express the integrand as
tan2θsecθ=sec2θ−1secθ.
However, we can directly integrate the expression as it is.