Question

Compute A′(1),A′(2) and A′(3).
A(x)=∫0x(5−t2)dt

Answer 1

To compute A′(1), A′(2), and A′(3), differentiate A(x) and substitute x = 1, 2, and 3 into A′(x).

Step-by-step explanation:

To compute A′(1), A′(2), and A′(3), we need to find the derivative of A(x).

Let's start by finding A(x).

A(x) = ∫0x(5 - t2)dt

Using the Fundamental Theorem of Calculus, we can differentiate A(x) to find A′(x).

A′(x) = 5 - x2

Now, we can substitute x = 1, 2, and 3 into A′(x) to find A′(1), A′(2), and A′(3).

A′(1) = 5 - 12 = 4

A′(2) = 5 - 22 = 1

A′(3) = 5 - 32 = -4