Question

Evaluate the indefinite integral ∫7x−1dx.

a) 7x²/2 −x+C
b) 7x²/2 +x+C
c) 7x²/2 −x² +C
d) 7x²/2 +x² +C

Answer 1

The correct evaluation of the indefinite integral ∫7x− 1dx is ½7x² − x + C.

Step-by-step explanation:

To evaluate the indefinite integral ∫7x−1dx, we apply basic rules of integration to each term separately. The integral of a constant multiple of x (∫ax dx) is ½ax², and the integral of a constant (∫ dx) is x. Applying these rules, we get:

1. The integral of 7x is ½(7)x², which simplifies to ½7x² or ¼7x².
2. The integral of −1 is −x.

Thus, the indefinite integral of 7x - 1 with respect to x is ½7x² − x + C, where C is the constant of integration.

The correct answer given the options is: a) ½7x² − x + C.