Integral Calculus

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Integration by Parts

Answer 4

Question 5

Area of a curve
Vertical strip:
Horizontal Strip:

Answer 5

Question 6

Volume of Solid Revolution
Rotated along the y-axis
rotated along the x-axis

Answer 6

Question 7

Volume of Solid Revolution
Rotated along the line parallel to the x-axis:
Rotated along the line parallel to the y-axis:

Answer 7

Question 8

Length of an arc (Integration)

Answer 8

Question 9

Surface Area of solid revolution
Rotated along the x-axis:
rotated along the y-axis:

Answer 9

Question 10

Volume below a curve using Pappus Theorem

Answer 10

Question 11

Average Value of a curve (Integration)

Answer 11

Question 12

Moment of area with respect to the y-axis:
Moment of area with respect to the x-axis:

Answer 12

Question 13

Coordinates of a centroid

Answer 13

Question 14

Centroid from vertex of a parabola (shortcut)

Answer 14

Question 15

-Moment of Inertia with respect to the y-axis:
-Moment of Inertia with respect to the x-axis:
-Polar Moment of Inertia:

Answer 15

Question 16

Area of a Polar coordinate curve (Integration)

Answer 16

Question 17

Length of Arc of a curve in polar form (Integration)

Answer 17

Question 18

(Integration)
Work of a
-Spring:
-Variable Load:

Answer 18

Question 19

(Integration)
Work of a
Pumping in or Pumping out of Liquid:

Answer 19

Question 20

Area of parabola bounded by the Latus Rectum

Answer 20

Question 21

Area of a parabolic segment

Answer 21

Question 22

Ways of solving integrating factor

Answer 22

Question 23

Exponential Growth formula

Answer 23

Question 24

Exponential Decay

Answer 24