Activity #1
Find the Anti derivative of the following polynomial functions.
1. The antiderivative of the f(x) = x2
Answer: F(x) = (1/3) x3 + C.
2. The antiderivative of f(x) = 3x^4
Answer: F(x) = (3/5) x5 + C.
3. The antiderivative of the f(x) = 2x3 + 5x2
Answer: F(x) = (1/2) x4 + (5/3) x3 + C.
4. The antiderivative of f(x) = 4x5 - 2x3 + x
Answer: F(x) = (2/3) x6 - (1/2) x4 + (1/2) x2 + C.
5. The antiderivative of f(x) = 2x3 + 7x2 - 3x + 1
Answer: F(x) = (1/2) x4 + (7/3) x3 - (3/2) x2 + x + C.
6. The antiderivative of f(x) = 6x2 - 4x + 9
Answer: F(x) = 2x3 - 2x2 + 9x + C.
7. The antiderivative of f(x) = 5x4 + 3x2 + 2x - 7
Answer: F(x) = x5 + x3 + x2 - 7x + C.
8. The antiderivative of f(x) = x3 - 2x + 4
Answer: F(x) = (1/4) x4 - x2 + 4x + C.
9. The antiderivative of f(x) = 2x5 + 3x4 - 5x3 + 2x2 - 9x + 6
Answer: F(x) = (1/3) x6 + (3/5) x5 - (5/4) x4 + (2/3) x3 - (9/2) x2 + 6x + C.
10. The antiderivative of f(x) = 7x6 - 5x4 + 2x3 - 3x2 + 8x – 1
Answer: F(x) = x7 - x5 + (1/2) x4 - x3 + 4 x2 - x + C.
Prepared by: Dr. JB Alegre