Evaluate the following, #int_0^1 (x^e +e^x) dx#. I know the anti-derivative of x^e is #x^(e+1)/(e+1)#. How would i solve this,would i use F(b) +F(a)?
1 Answer
Jan 15, 2017
I got
The correct answer is:
# int_0^1 (x^e+e^x) \ dx = 1/(e+1)+e - 1#
Explanation:
I did F(1)-F(0) and i did anti-derivative of x^e * derivative of x^e which is
Where we used:
#1^n = 1 AA n in RR \ \ \ \ \ \ \ \ \ \ \ => 1^(e+1)=1#
#0^n=0 AA n in RR-{0} \ => 0^(e+1)#
#x^n=1 AA n in RR \ \ \ \ \ \ \ \ \ \ \ => e^0 = 1#