Welcome :: Homework Help and Answers :: Mathskey.com
Welcome to Mathskey.com Question & Answers Community. Ask any math/science homework question and receive answers from other members of the community.

13,435 questions

17,804 answers

1,438 comments

774,941 users

Integration and Area

0 votes

Question 1

Question 2

Question 3

Question 4

asked Sep 19, 2014 in CALCULUS by zoe Apprentice

8 Answers

0 votes
 
Best answer

(4b)

image

Apply integration by parts  ∫u v dx = u∫v dx −∫u' (∫v dx) dx

Let u = t+1 , v =√t ⇒ u' = 1

image

answered Sep 20, 2014 by friend Mentor
selected Sep 21, 2014 by zoe
0 votes

(1)

Acceleration of object is a(t) = 3t + 5 m/s²

Acceleration is the rate of change in velocity a(t) = dv/dt

image

We want to find the velocity v(t)

image

Given v(0) = 3 m/s

image

But we have to calculate velocity during the time interval 0 ≤ t ≤ 1

image

So velocity v(t) = 6.5 m/s

Velocity is the rate of change in distance or displacement v(t) = ds /dt

image

We have to calculate distance during the time interval 0 ≤ t ≤ 1

image

So velocity is 6.5 m/s and distance is 6m

answered Sep 19, 2014 by friend Mentor
0 votes

(2)

Rate of change of volume is dv/dt  = 100 - ( t - 11)²

image

Given v = 250 lt when t = 0 means that V(0) = 250

image

Water in storage tank after 3 days is v(3)

image

Water in storage tank after 3 days 277 litres

Water in storage tank after 6 days is v(6)

image

Water in storage tank after 6 days is 448 litres 

answered Sep 19, 2014 by friend Mentor
0 votes

(3a)

The area of the region bounded by the the function f(x) = cos x ,the x-axis,

and the vertical lines x = a and x = b : image  

The function f(x) = cos x and vertical lines x = π/4 and x = π

image

      = 0.7071

Area of the region bounded by the the function f(x) = cos x and  x-axis is  0.7071

answered Sep 20, 2014 by friend Mentor
edited Sep 21, 2014 by bradely
0 votes

(4a)

The given integral is image

image

answered Sep 20, 2014 by friend Mentor
0 votes

(4c)

image

Now spilt the fraction

image

answered Sep 20, 2014 by friend Mentor
0 votes

(4d)

image

Now spilt the fraction

image

 

answered Sep 20, 2014 by friend Mentor
0 votes

(4e)

image

Now spilt the terms and perform integration

image

answered Sep 20, 2014 by friend Mentor

Related questions

...