ユ Find the integral. dx

Q: eSz sin(6x)dx —

A: For the  I=∫eaxsin(bx) dx =eaxa2+b2asin(bx)-bcos(bx)+C (Using integration by parts)

Q: 14.1 dx V16-x dx 15. . Vx -1

A:

Q: 3.S dx C. ez? D. ex А. х В.-х? cos x 4. S9 dx V1+sin x A. V1+sinx B. cosx C. sinx D. 1+ sinx

A:

Q: Evaluate the integral. dx 4 - x3

A:

Q: Evaluate the integral. dx

A: Here given

Q: Find the integral. -3 4Vx dx X.

A: Given,        ∫-3x3-4xdx

Q: Solve the integral. cos x dx J (1+ sin² x) arctan (sin x) 10.

A: To evaluate:                      ∫cos x(1+sin2 x)arctan(sin x)dx    ... (1)

Q: Evaluate the integral. Answer= +C -22e-30 e2x + 6e +5 12276 -da

A:

Q: 1 I. 1+ Vx xp:

A:

Q: Evaluate the integral. LG 5t4 -k dt 1 + t5 1 + t

A: The given integral is: I=∫01 51+t2 j + 5t41+t5 k  dt

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: