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Find the are under the given curve

y=square root of x + 1
from x=0 to x=9

Please walk me through each step.

Do you mean sqrt(x+1) or sqrt x + 1?

If the former, the indefinite integral is [(x+1)^3/2]/(3/2)
Evaluate it at x = 9 and x = 0 and take the difference.

Area = (2/3)*[(10)^(3/2) - 1]

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Did you know?

Did you know that finding the area under a curve can be done through a process called integration? In this case, we have the curve y = square root of x + 1. To find the area under this curve from x = 0 to x = 9, we will follow these steps: 1. Start by determining the integral expression. Since we want to find the area, we integrate the function with respect to x: ∫(square root of x + 1) dx. 2. Simplify the integral expression. We can rewrite the square root of x + 1 as (x + 1)^(1/2). The integral becomes ∫(x + 1)^(1/2) dx. 3. Integrate the expression. Using the power rule of integration, we can integrate (x + 1)^(1/2) to get (2/3)(x + 1)^(3/2) + C, where C represents the constant of integration. 4. Evaluate the definite integral. To find the area under the curve from x = 0 to x = 9, we subtract the integral's value at x = 0 from the integral's value at x = 9: [(2/3)(9 + 1)^(3/2) + C] - [(2/3)(0 + 1)^(3/2) + C]. 5. Calculate the final result. By plugging the values into the equation and simplifying, we can determine the area under the curve from x = 0 to x = 9. Remember, integration allows us to find the area under curves, providing a useful tool in various fields such as mathematics, physics, and engineering.