Download presentation

Presentation is loading. Please wait.

Published byStephen Ryan Modified over 7 years ago

1
Integral calculus XII STANDARD MATHEMATICS

2
Evaluate: Adding (1) and (2) 2I = 3 I = 3/2

3
Evaluate: Adding (1) and (2)

4
Evaluate: Adding (1) and (2)

5
Evaluate: Let u = x/4, then dx = 4du When x = 2 , u = /2 When x = 0, u = 0

6
Find the area of the circle whose radius is a. Equation of the circle whose center is origin and radius a units is x 2 + y 2 = a 2. Since it is symmetrical about both the axes, The required area is 4times the area in the first quadrant. x y The required area =

7
Find the area of the region bounded by the line y = 2x + 4, y = 1, y = 3 and y-axis The required area lies to the left of y axis between y = 1 and y = 3 x y y =1 y =3 y =2x+3 The required area = = 2sq.units

8
Find the area of the region bounded by x 2 = 36y, y-axis, y = 2 and y = 4. The required area lies to the right of y-axis between y = 2 and y = 4 x y y = 2 y = 4 x 2 = 36y The required area =

9
Find the volume of the solid that results when the ellipse (a > b > 0)is revolved about the minor axis. The required volume is twice the volume obtained by revolving the area in the first quadrant about the minor axis (y-axis) between y = 0 and y = b x y The required volume =

10
Find the area between the curve y = x 2 –x – 2, x-axis, and the lines x = – 2, x = 4 Equation of the curve is y = x 2 – x – 2 When y = 0, x 2 – x – 2 = 0 (x – 2)(x + 1) = 0 x = 2, – 1 The curve cuts x-axis at x = –1 and x = 2 The required area = A 1 + A 2 + A 3 Where A 1 is area above the x-axis between x = –2 and x = –1 A 2 is area below the x-axis between x = –1 and x = 2 A 3 is area above the x-axis between x = 2 and x = 4 The required area = x y x=4 x=-2

12
Find the area enclosed by the parabolas y 2 = x and x 2 = y Equation of the parabolas are y 2 = x………(1) = f(x) x 2 = y………(2) = g(x) Sub (2) in (1) (x 2 ) 2 = x x 4 – x = 0 x(x 3 – 1) = 0 x = 0, 1 If x = 1, y = 1 The point of intersection is (1, 1) The required area = area between the two curves from x = 0 to x = 1 Required area = x y y 2 = x x 2 = y x=1

Similar presentations

© 2023 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google