Question

Find each of the following indefinite integrals.

∫ (4x² – 3√x + 2) dx
a) 4/3 x^3 - 2x^(3/2) + 2x + C
b) x^3 - 2x^(3/2) + 2x + C
c) (4/3)x^3 - (2/3)x^(3/2) + 2x + C
d) (1/3)x^3 - 2x^(3/2) + 2x + C

Answer 1

The correct indefinite integral of the function 4x² – 3√x + 2 is (4/3)x³ - (2/3)x³² + 2x + C.

Step-by-step explanation:

The student has asked to find the indefinite integral of the function f(x) = 4x² – 3√x + 2. To do so, we integrate each term separately.

• For the first term 4x², the integral is (4/3)x³.
• For the second term -3√x (which is the same as -3x¹²), the integral is -2x³².
• For the constant term 2, the integral is 2x.

Combining all these, we get the integral (4/3)x³ - 2x³² + 2x + C, where C is the constant of integration.

Therefore, the correct answer is c) (4/3)x³ - (2/3)x³² + 2x + C.