00:02
So, evaluate the line to grow.
00:07
Here, we compute, again, like the previous problem, we compute f of r of t, and we compute r prime of t, and we take the dot product and integrate it, and where t, the lower bond and upper bond is 0 and 1.
00:31
So x is t cubed, so we have this.
00:36
Y is negative t square, but cosine is an even function, so negative t squared, cosine negative t squared and no cosine t squared is the same thing.
00:47
Xz is t to the fourth, derivative is 3t square minus 2 t 1.
00:57
So we integrate from 0 to 1 and their product.
01:01
So 3 t squared sine t cubed minus 2 t cosine, t squared plus t to the 4 d t and the antiderivative you should be able to see that this is a straightforward u sub problem the tq equals u then this part is d u so this this should be negative cosine t q and similarly this should be negative sine t squared and similarly this should be negative sine t square and plus t to the fifth over 5...