Find h(x)h\left(x\right)h(x) by evaluating the following indefinite integral.h(x)=∫x8dxh\left(x\right)=\int x^8dxh(x)=∫x8dx

h ( x ) = x 9 9 + C h\left(x\right)=\frac{x^9}{9}+C h ( x ) = 9 x 9 + C

Find h ( x ) h\left(x\right) h ( x ) by evaluating the following indefinite integral. h ( x ) = ∫ x 8 d x h\left(x\right)=\int x^8dx h ( x ) = ∫ x 8 d x

this problem, we're asked to find the function h of x by evaluating the following integral. Now here we have the integral of x to the 8th with respect to x. And recall that we learned through this power rule, where all we can do is take whatever we have in here, If we have this type of power function, we can add 1 to the exponent and then divide everything by that new exponent. So doing this, we would get x to the 8 plus 1, which is 9, divided by 8 plus 1, which is 9. And don't forget you always wanna add the constant of integration c whenever you do this type of process. So this right here would be the solution to this function. Hope you found this video helpful.

Find h ( x ) h\left(x\right) h ( x ) by evaluating the following indefinite integral. h ( x ) = ∫ x 8 d x h\left(x\right)=\int x^8dx h ( x ) = ∫ x 8 d x

h ( x ) = x 9 9 + C h\left(x\right)=\frac{x^9}{9}+C h ( x ) = 9 x 9 + C

h ( x ) = x 9 + C h\left(x\right)=x^9+C h ( x ) = x 9 + C

h ( x ) = x 9 9 h\left(x\right)=\frac{x^9}{9} h ( x ) = 9 x 9

h ( x ) = x 9 h\left(x\right)=x^9 h ( x ) = x 9

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

Business Calculus

7. Antiderivatives & Indefinite Integrals

Indefinite Integrals

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Multiple Choice

Find $h\left(x\right)$ by evaluating the following indefinite integral.
$h\left(x\right)=\int x^8dx$

$h\left(x\right)=x^9+C$

$h\left(x\right)=\frac{x^9}{9}+C$

$h\left(x\right)=\frac{x^9}{9}$

$h\left(x\right)=x^9$

Verified step by step guidance

Step 1: Recognize that the problem involves finding the indefinite integral of the function x^8. The general formula for the indefinite integral of x^n is ∫x^n dx = (x^(n+1))/(n+1) + C, where n ≠ -1.

Step 2: Identify the exponent of x in the given function. Here, the exponent is 8, so n = 8.

Step 3: Apply the formula for the indefinite integral. Substitute n = 8 into the formula, which gives (x^(8+1))/(8+1) + C = (x^9)/9 + C.

Step 4: Simplify the expression to write the result in its final form. The integral of x^8 is (x^9)/9 + C, where C is the constant of integration.

Step 5: Conclude that the function h(x) is h(x) = (x^9)/9 + C, which represents the indefinite integral of x^8.

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