Question

2 If ∫ sec²(7 – 4x)dx = a tan (7 – 4x) + C, then value of a is​

Answer 1

Step-by-step explanation:

We have,

$\int \sec^{2} (7 - 4x) dx = a \tan( 7 - 4x) + c$

$let \: ( 7 - 4x) = t \\ \implies - 4dx = dt$

$- \frac{1}{4} \int \sec^{2} (t) dt = a \tan(7 - 4x) + c$

$\implies - \frac{1}{4} \tan(7 - 4x) + c = a \tan(7 - 4x) + c$

$\implies \: a = - \frac{1}{4}$