Please help with the questions on definite integrals.

[Haru]

Hello, I am Haru and I have difficulties to solve the following problems. It would be much appreciated if someone can help me. Sorry for asking so many questions. And wish you Merry Christmas.

Suppose that ∫f(t)dt=17 (which the lower bound (from): 0 and the upper bound (to): 1). Calculate each of the following:
(a.) ∫f(4t)dt=? (which the lower bound (from): 0 and the upper bound (to): 0.25)
(b.) ∫f(1−8t)dt= ? (which the lower bound (from): 0 and the upper bound (to): 0.125)
(c.) ∫f(5−2t)dt= ? (which the lower bound (from): 2 and the upper bound (to): 2.5)

For these questions, I have no idea to start answering.

 

[Deleted member 4993]

Hello, I am Haru and I have difficulties to solve the following problems. It would be much appreciated if someone can help me. Sorry for asking so many questions. And wish you Merry Christmas.

Suppose that ∫f(t)dt=17 (which the lower bound (from): 0 and the upper bound (to): 1). Calculate each of the following:
(a.) ∫f(4t)dt=? (which the lower bound (from): 0 and the upper bound (to): 0.25)
(b.) ∫f(1−8t)dt= ? (which the lower bound (from): 0 and the upper bound (to): 0.125)
(c.) ∫f(5−2t)dt= ? (which the lower bound (from): 2 and the upper bound (to): 2.5)

For these questions, I have no idea to start answering.

(a) Use substitution

u = 4t ....................................................(don't forget to change the limits of integration)

(b) Use substitution

u = 1 - 8t .....................................................(Watch the limits of integration)

(b) Use substitution

u = 5 - 2t .....................................................(Watch the limits of integration)