Please how do i integrate this = ¡Ò (5 x⁶ + 2/x³ ) ? Thanks
what is the derivative of (5/7)x^7 ?
what is the derivative of -x^(-2) ?
Yeah.. Thanks Damon! I now have an idea of how to go about that.
But if you don't mind..can you give me an idea on how to go about this problem also? Solve ¡Ò 2(2x -3)�0…5/�0…6
Do you mean from 0 to 5 and from 0 to 6 ?
if so
2 (x^2 -3 x) at 5 - at 0
= 2 (25 - 15) - 0
= 20
at6 it is 2 (36-18) = 2*18 = 36
To integrate the function ¡Ò (5 x⁶ + 2/x³), you can follow these steps:
Step 1: Identify the terms
In your function, we have two terms: 5x⁶ and 2/x³.
Step 2: Apply the power rule
To integrate each term, we can use the power rule. The power rule states that when integrating a term of the form xⁿ, you add 1 to the exponent and divide by the new exponent.
For the first term, 5x⁶, we add 1 to the exponent to get x⁷, and then divide by the new exponent: (5/7) x⁷.
For the second term, 2/x³, we add 1 to the exponent to get x⁴, and then divide by the new exponent: (2/4) x⁴ = (1/2) x⁴.
Step 3: Combine the terms
After integrating each term separately, you can combine them to get the final result. In this case, the integral of the given function, ¡Ò (5 x⁶ + 2/x³), is:
(5/7) x⁷ + (1/2) x⁴ + C
where C is the constant of integration.
So, the final answer to the integration is (5/7) x⁷ + (1/2) x⁴ + C.