Will mark brainliest if correct :)
1 answer:
You might be interested in
Answer:
g(x)=x^3+2x^2 - 4
Step-by-step explanation:
See attached worksheet
Let . Then
for all
, so
is strictly increasing. As
,
, so
is bounded above by 1. This is to say,
and the integral of converges over the same domain, so this integral must also converge by comparison.
We have, by setting ,
Answer:
Using either method, we obtain:
Step-by-step explanation:
a) By evaluating the integral:
The integral itself can be evaluated by writing the root and exponent of the variable u as:
Then, an antiderivative of this is:
which evaluated between the limits of integration gives:
and now the derivative of this expression with respect to "t" is:
b) by differentiating the integral directly: We use Part 1 of the Fundamental Theorem of Calculus which states:
"If f is continuous on [a,b] then
is continuous on [a,b], differentiable on (a,b) and
Since this this function is continuous starting at zero, and differentiable on values larger than zero, then we can apply the theorem. That means: