Evaluate each integral using the definit

Question

Evaluate each integral using the definition of the definite integral with right endpoints (given in Theorem 4 of the book) and taking the limit. (Note: If all you do is take the antiderivative and get the answer, you will get 0 points for these problems. You need to write out the Riemann sum and use the summation formulas.)
(a) ³∫₀(x² +2x–5]dx
     △x=(b-a)/n=
       xᵢ=a + i△x=

(b)  ₁∫⁵ x³dx
       △x=(b-a)/n=
       xᵢ=a + i△x=

Kunduz · Accepted Answer

3
Sol?
o
cach.
s (x² + 2x-5) dx
(
We know that for a
subinterval is
Ax = 6-a -
the width of a
general in
3-0
n
3
n
The subintervals are
then,
[; }] [], [2], -- ., 536-1],
0,
120,-
2
3 (n-1) 3
3
2
n
we
see
है
As
can
the right endpoint of the ith
subinterval is
x =
3i
The summation in the definition of the definite
integral
Ž f(xi) An
is then
1(33)
1
(A) + २(35)-5) (2)