Let

Integrate by parts, taking
<em>u</em> = <em>x</em> ==> d<em>u</em> = d<em>x</em>
d<em>v</em> = sin<em>ᵐ </em>(<em>x</em>) d<em>x</em> ==> <em>v</em> = ∫ sin<em>ᵐ </em>(<em>x</em>) d<em>x</em>
so that

There is a well-known power reduction formula for this integral. If you want to derive it for yourself, consider the cases where <em>m</em> is even or where <em>m</em> is odd.
If <em>m</em> is even, then <em>m</em> = 2<em>k</em> for some integer <em>k</em>, and we have

Expand the binomial, then use the half-angle identity

as needed. The resulting integral can get messy for large <em>m</em> (or <em>k</em>).
If <em>m</em> is odd, then <em>m</em> = 2<em>k</em> + 1 for some integer <em>k</em>, and so

and then substitute <em>u</em> = cos(<em>x</em>) and d<em>u</em> = -sin(<em>x</em>) d<em>x</em>, so that

Expand the binomial, and so on.
Answer:
1/2
Step-by-step explanation:
Answer:
Hence, option: B is correct (11.02 seconds)
Step-by-step explanation:
Spencer hits a tennis ball past his opponent. The height of the tennis ball, in feet, is modeled by the equation h(t) = –0.075t2 + 0.6t + 2.5, where t is the time since the tennis ball was hit, measured in seconds.
Now we are asked:
How long does it take for the ball to reach the ground?
i.e. we have to find the value of t such that height is zero i.e. h(t)=0.

or 
i.e. we need to find the roots of the above quadratic equation.
on solving the equation we get two roots as:
t≈ -3.02377 and t≈11.0238
As time can't be negative; hence we will consider the value of t as t≈11.0238.
Hence it takes 11.02 seconds for the ball to reach the ground.
Hence option B is correct (11.02 seconds).
Answer:
6
Step-by-step explanation: