`int_0^1 (x^10 + 10^x) dx` Evaluate the integral

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to evaluate the integral, hence, you need to use the fundamental theorem of calculus, such that:

`int_a^b f(x)dx = F(b) - F(a)`

`int_0^1(x^10 + 10^x)dx = int_0^1(x^10)dx + int_0^1 10^x dx`

Evaluating each definite integral, yields:

`int_0^1(x^10)dx = (x^10)/10|_0^1 = (1/10)(1^10 - 0^10) = 1/10`

`int_0^1 10^x dx = (10^x)/(ln 10)|_0^1 = (10^1)/(ln 10) - (10^0)/(ln 10)`

`int_0^1 10^x dx =1/(ln 10)(10 - 1) = 9/(ln 10)`

Hence, evaluating the definite integral, using the fundamental theorem of calculus yields `int_0^1(x^10 + 10^x)dx = 1/10 + 9/(ln 10).`

Access hundreds of thousands of answers with a free trial.

Start Free Trial
Ask a Question