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Integration upper limit 2 lower limit minus 2 (x power 2019) dx is equal to |
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Answer» Step-by-step EXPLANATION: We know that ∫ a b
f(x)dx=(b−a) N→∞ lim
n 1
(f(a)+f(a+h)+...+f(a+(n−1)h)) Putting a=0,b=2,h= n b−a
= n 2−0
= n 2
in ∫ 0 2
x 2 +1dx I=(2−0) n→∞ lim
n 1
(f(0)+f(n)+f(2n)+...+f((n−1)h)) f(0)=1 f(h)=h 2 +1 =( n 2
4
)+1 f((n−1)h)=(n−1) 2 × n 2
4
+1 ∴I=2 n→∞ lim
n 1
((1+1+...ntimes)+(0+ n 2
4
+ n 2
16
+...+ n 2
(n−1) 2
)) =2 n→∞ lim
n 1
(n+ n 4
6 (n−1)n(2n−1)
) =2 n→∞ lim
(1+ 3 2
(1− n 1
)(2− n 1
)) =2×(1+ 3 4
)= 3 14
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