Answer:
1/4 of the cake.
Step-by-step explanation:
Since he ate 1/3 of 3/4 of the chocolate cake, we will need to multiply fractions to solve this.
Therefore, he ate 1/4 of the entire cake.
2 1/3. 3 inches by 2 1/3 inches is 7. A 3rd of that is 2 1/3 or 2.3333333333
Answer:
Step-by-step explanation:
So we have the indefinite integral:
This is the same thing as:
So, let's do integration by parts.
Let u be (ln(x))². And let dv be (1)dx. Therefore:
Simplify:
And:
Therefore:
The x cancel:
Move the 2 to the front:
(I'm not exactly sure how you got what you got. Perhaps you differentiated incorrectly?)
Now, let's use integrations by parts again for the integral. Similarly, let's put a 1 in front:
Let u be ln(x) and let dv be (1)dx. Thus:
And:
So:
Simplify the integral:
Evaluate:
Now, we just have to simplify :)
Distribute the -2:
And if preferred, we can factor out a x:
And, of course, don't forget about the constant of integration!
And we are done :)