
Setting

, you have

. Then the integral becomes




Now,

in general. But since we want our substitution

to be invertible, we are tacitly assuming that we're working over a restricted domain. In particular, this means

, which implies that

, or equivalently that

. Over this domain,

, so

.
Long story short, this allows us to go from

to


Computing the remaining integral isn't difficult. Expand the numerator with the Pythagorean identity to get

Then integrate term-by-term to get


Now undo the substitution to get the antiderivative back in terms of

.

and using basic trigonometric properties (e.g. Pythagorean theorem) this reduces to
Answer:
15 feet.
Step-by-step explanation:
Tony's speed = 15 ft/min.
Antonio's = 18 feet /min.
So in 5 minutes Tony travels 5*15 = 75 feet and Antonio travels 5*18 = 90 feet.
So the answer is 90-75 = 15 feet.
The answer should be -5x + 7y = -108
Answer:
Total cost, c = 7p
Step-by-step explanation:
1pound =$7
Joe buys p pounds,
p pounds = $7 * p
p pounds = 7p