Question

How do you do this question?

Answer 1

Answer:

Correct integral, third graph

Step-by-step explanation:

Assuming that your answer was 'tan³(θ)/3 + C,' you have the right integral. We would have to solve for the integral using u-substitution. Let's start.

Given : ∫ tan²(θ)sec²(θ)dθ

Applying u-substitution : u = tan(θ),

=> ∫ u²du

Apply the power rule ' ∫ xᵃdx = x^(a+1)/a+1 ' : u^(2+1)/ 2+1

Substitute back u = tan(θ) : tan^2+1(θ)/2+1

Simplify : 1/3tan³(θ)

Hence the integral ' ∫ tan²(θ)sec²(θ)dθ ' = ' 1/3tan³(θ). ' Your solution was rewritten in a different format, but it was the same answer. Now let's move on to the graphing portion. The attachment represents F(θ). f(θ) is an upward facing parabola, so your graph will be the third one.