# Find the Area under the Curve: y = 9/x^{3} from x = 1 to x = t.

We will be using the area under the curve formula to solve this.

## Answer: The Area under the Curve, y = 9/x^{3} from x = 1 to x = t is 9/2 (1 - 1/t^{2})

Let's solve this step by step to the area under the given curve.

**Explanation:**

Given that, y = 9/x^{3} from x = 1 to x = t

The area under the curve formula: Area** **Under The Curve = ∫_{a}^{b} f(x) dx

Here, a and b are the limit of integration.

Here, a = 1 and b = t.

Area** **Under The Curve = ∫_{1}^{t} 9/x^{3} dx

= 9 ∫_{1}^{t} x^{-3} dx

= 9 [-1/2 x^{-2}]_{1}^{t}

= -9/2 (t)^{-2} - (-9/2 .{1}^{-2})

= -9/2 t^{-2} + 9/2

= 9/2(1 - 1/t^{2})