Integrals In Geometry And Trigonometry

Question 1

Finding trapezoids with values of a and b simplified.

Answer 1

Integral(a,b)xox=(b^2-a^2)/2

Question 2

Areas between functions of integration

Answer 2

Integral(a,b)f(x)dx-integral(a,b)g(x)dx

Question 3

INtegrals bound by the x axis and two lines.

Answer 3

Integral(a,d) f(x)-g(x)dx + integral(b,d)f(x)dx

Question 4

Volume of a cone

Answer 4

Integral(a,b)A(x)dx

Question 5

Washer method of integration

Answer 5

Integral(a,b)pi(router(x)^2]-[rinner(x)]^2dx

Question 6

Trig integrals.

Answer 6

Claims that if you know integral of sin(x) and integral of cos(x) will help you solve a lot of them.

Question 7

Trig substitutions

Answer 7

C^2+x^2 use x=ctantheta. Trig sub 1+tan^2theta=sec^2theta

C^2-x^2. Use x=chin theta. Trig sub 1-sin^2theta=cos^2theta

X^2-c^2 use x-cSectheta. sec^2theta-1=tan^2theta.