For the first on note that , and since the derivative of cos(t) is -sin(t) we can say the derivative of is .
So your integral becomes... .
1. Use the First Fundamental Theorem of Calculus to find the derivative of
=???
2. Consider the function .
In this problem you will calculate by using the definition
The summation inside the brackets is which is the Riemann sum where the sample points are chosen to be the right-hand endpoints of each subinterval. Calculate for on the interval and write your answer as a function of without any summation signs.
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( So on this one I did: f(Xk)=f(x)= x^2/2+7) then plug in (2/n *k) for x and got 4/2n^2*k^2+7.
then (4/2n^2*k^2+7) * 2/n and got (8/2n^3*k^2+14/n).
8/2n^3*(2n^3+3n^2+n)= 16n^3+24n^2+8n/12n^3 + 14 answer. did i do something wrong?
For the second part: i took the antiderivative of and evaluate from 0 to 3. the answer i got is (27/6+7). Help me out thanks.
3.
and
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The absolute maximum of occurs when ??? and is the value =????