wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

Evaluate 10e23xdx as a limit of a sum.

Open in App
Solution

Let I=10e23xdx
It is known that,
baf(x)dx=(ba)limn1n[f(a)+f(a+h)+...+f(a+(n1)h]
Where, h=ban
Here, a=0,b=1, and f(x)=e23x
h=10n=1n
10e23xdx=(10)limn1n[f(0)+f(0+h)+...+f(0+(n1)h)]
=limn1n[e2+e23h+....e23(n1)h]
=limn1n[e2{1+e3h+e6h+e9h+...e3(n1)h}]
=limn1n[e2{1(e3h)n1(e3h)}]
=limn1n[e2{1e3n×n1e3n}]
=limn1ne2(1e3)1e34
=e2(e31)limn1n[1e3n1]
=e2(e31)limn(13)[3ne3n1]
=e2(e31)3limn[3ne3n1]
=e2(e31)3(1)[limnxex1]
=e1+e23
=13(e21e)

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Factorisation and Rationalisation
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon