How do you do this question?

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

Step-by-step explanation:

∫ 15 sin(√(at)) dt

Use substitution:

If x = √(at), then:

dx = ½ (at)^-½ (a dt)

dx = a / (2√(at)) dt

dx = a/(2x) dt

dt = (2/a) x dx

Plugging in:

∫ 15 sin x (2/a) x dx

30/a ∫ x sin x dx

Integrate by parts:

If u = x, then du = dx.

If dv = sin x dx, then v = -cos x.

∫ u dv = uv − ∫ v du

= 30/a (-x cos x − ∫ -cos x dx)

= 30/a (-x cos x + ∫ cos x dx)

= 30/a (-x cos x + sin x + C)

Substitute back:

30/a (-√(at) cos(√(at)) + sin(√(at)) + C)

-30√(t/a) cos(√(at)) + 30/a sin(√(at)) + C

at first, in 1635, the evening meetings had been just for women . .

what relationship between ideas is shown in the text above?

question 1 options:

location of events

similarity of events

timing of events

examples of an idea

step-by-step explanation:

good luck on your studies! : )

david edward.