Integral Calculus

Question 1

The reverse process of differentiation

Answer 1

Integration

Question 2

Definite Integrals

Answer 2

Cal Tech

Directly input the equation with respect to a given variable.

Question 3

Indefinite Integral

Answer 3

Cal Tech

Compare the derivatives of the choices to the given equation inside integral sign

Question 4

It is called Antiderivative / Primitive Integral

Answer 4

Indefinite Integrals

Question 5

Elongated S sign used in integration

Answer 5

Summa

Question 6

Integral that is defined by the limit values

Answer 6

Definite Integral

Question 7

Area

Answer 7

stripping perpendicular to x axis

A = ∫ ydx

stripping perpendicular to y axis

A = ∫ xdy

Question 8

Polar Area

Answer 8

A = ∫ (r^2)/2 dθ

Question 9

Cetroid

Answer 9

stripping perpendicular to x axis

Xbar = ∫ x dA / A

Ybar = ∫ (y/2) dA / A

Question 10

Length of Arc

Answer 10

stripping perpendicular to x axis

S = ∫sqrt(1+(dy/dx)^2) dx

stripping perpendicular to y axis

S = ∫sqrt(1+(dx/dy)^2) dy

Question 11

Surface Area

Answer 11

A = ∫ 2πr dS

Question 12

Volume using Second Proposition of Pappus

Answer 12

V = ∫ 2πr dA

Question 13

Shell Method

Answer 13

stripping perpendicular to x axis

V = ∫ 2πyx dx

Question 14

Ring Method / Washer Method

Answer 14

stripping perpendicular to x axis

V = ∫ π(yu^2 - yl^2)dx

Question 15

Work

Answer 15

Work = ∫ F dx

Question 16

Work done by Spring

Answer 16

F = kx
W =  ∫ kx dx

Question 17

Moment of Inertia

Answer 17

stripping perpendicular to x axis

Ix = ∫ y^2 dA

Iy = ∫ (x/2)^2 dA

Question 18

Multiple integral

Answer 18

Integrate Inner equations first then proceed integrating outwards