To evaluate the integral of the square root of x with respect to x, you can use the power rule for integration. The power rule states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Here are the steps:

1. Rewrite the square root of x as x^(1/2).
2. Apply the power rule. Increase the exponent by 1 to get 1/2 + 1 = 3/2. Then divide by the new exponent: (1/(3/2))x^(3/2).
3. Simplify the fraction: (2/3)x^(3/2).
4. Add the constant of integration: (2/3)x^(3/2) + C.

So, ∫x^(1/2) dx = (2/3)x^(3/2) + C.

Question

To evaluate the integral of the square root of x with respect to x, you can use the power rule for integration. The power rule states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Here are the steps:

1. Rewrite the square root of x as x^(1/2).
2. Apply the power rule. Increase the exponent by 1 to get 1/2 + 1 = 3/2. Then divide by the new exponent: (1/(3/2))x^(3/2).
3. Simplify the fraction: (2/3)x^(3/2).
4. Add the constant of integration: (2/3)x^(3/2) + C.

So, ∫x^(1/2) dx = (2/3)x^(3/2) + C.

Knowee AI · Accepted Answer

To evaluate the integral of the square root of x with respect to x, you can use the power rule for integration. The power rule states that the integral of x^n dx is (1/(n+1))x^(n+1) + C, where C is the constant of integration.

Here are the steps:

1. Rewrite the square root of x as x^(1/2).
2. Apply the power rule. Increase the exponent by 1 to get 1/2 + 1 = 3/2. Then divide by the new exponent: (1/(3/2))x^(3/2).
3. Simplify the fraction: (2/3)x^(3/2).
4. Add the constant of integration: (2/3)x^(3/2) + C.

So, ∫x^(1/2) dx = (2/3)x^(3/2) + C.

Evaluate the following.∫𝑥‾‾√d𝑥=

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