COMEDK2025MathematicsIndefinite IntegrationActual
7^ 2 x d x= (x)+c then (x)=
Options
- A7^ 2 x 7
- B7^ 2 x 2 7
- C1
- D7^ 2 x 7
Correct answer
B. 7^ 2 x 2 7
Step-by-step solution
The integral to be evaluated is I = 7^ 2x dx . Using the standard integration formula a^ u du = a^ u a + c , where a = 7 and u = 2x . Since u = 2x , du = 2 dx , which implies dx = du 2 . Substituting these into the integral: I = 7^ u du 2 = 1 2 7^ u du . I = 1 2 ( 7^ u 7 ) + c . Substituting u = 2x back into the expression: I = 7^ 2x 2 7 + c . Since 7 = _ e 7 , which is often denoted as 7 in this context, we have (x) = 7^ 2x 2 7 . Answer: 7^ 2 x 2 7