What is the antiderivative of f(x)= 2x^8 + 10x^5 - 8x^4 - 4?
I got (2/9)^9 + (10/6)^6 - (8/5)^5 - 4x but it's not right.
Your answer is correct.
Check your second term, they probably reduced the 10/6 to 5/3
What happened to the x's in the first three terms?
The first term should be (2/9)x^9
You made similar errors in the second and third terms by not typing in the "x" before the exponent.
drwls is right.
I didn't even notice that you dropped the x's.
Oh dang. That's what I forgot. The x's. I put in the x's and the answer was correct. Thanks!
To find the antiderivative of a function, you need to apply the power rule and the constant rule of integration. Let's break down the process step by step.
Given f(x) = 2x^8 + 10x^5 - 8x^4 - 4, we can find the antiderivative term by term.
1. For the term 2x^8, apply the power rule. The power rule states that the antiderivative of x^n is (1/(n+1)) * x^(n+1). According to this rule, the antiderivative of 2x^8 is (2/(8+1)) * x^(8+1) = (2/9) * x^9.
2. For the term 10x^5, apply the power rule again. The antiderivative of 10x^5 is (10/(5+1)) * x^(5+1) = (10/6) * x^6.
3. For the term -8x^4, we once again apply the power rule. The antiderivative of -8x^4 is (-8/(4+1)) * x^(4+1) = (-8/5) * x^5.
4. Finally, for the constant term -4, remember that the antiderivative of any constant is simply the constant times x. Therefore, the antiderivative of -4 is -4x.
Now, summing up all the antiderivatives we found, the antiderivative of f(x) = 2x^8 + 10x^5 - 8x^4 - 4 is:
(2/9) * x^9 + (10/6) * x^6 - (8/5) * x^5 - 4x.
It seems that there might have been a mistake in your calculations. Double-check your work to make sure all the derivatives and constants were carried out correctly.