How to integrate #int_(1"/"2)^1 4^x "d"x#?
2 Answers
Explanation:
The trick part about this integral is that we don't know the exponential function with base 4 very well.
Rewrite
And now, it's easier to find an antiderivative.
Although you could make a substitution, it can be quicker to do this in your head. Consider the derivative of
We can see that if we divide both sides by the constant
We can simplify the antiderivative. Let
Now that we have the antiderivative, can substitute the upper and lower bounds as follows.
Explanation:
Let
Then
Also,
Thus