Find dy /dx ; for the following (sec 2x) )ه( (cos

Q: ƒ7 In ()dx if sec¹ (3x) dx

A: Integration by parts: ∫f(x)·g(x) dx = f(x)·∫g(x) dx - ∫ddxf(x)·∫g(x) dx dx

Q: sin(cos¬1/2x²) = v3x? sO:

A: Given:   SinCos-1 2x2=3x2   To find out: x=?

Q: | (5cotx – sin x) csc² x dx

A: Given integral is: ∫5cotx-sinxcsc2xdx Rewriting the integral:…

Q: is If У%3D2х arccos x - 2/1-х? then dx

A: We differentiate both sides with respect to x and then solve it.

Q: 11. cos4x-cos2 dx sin4x-cos2x

A:

Q: sinx dx TI cosx t ecoSX 2

A:

Q: sin (x²)dxdy y

A: We will solve this question by change of order of integration.

Q: Se-*cos(5x) dx

A: Given : ∫ e−xcos(5x)dx

Q: Find d coscrin' (-2] the exact value

A: Find the exact value cossin-25.

Q: Evaluate

A:

Q: 3 S (sin x)*.dx

A: Please refer the attached image for complete solution.

Q: dy If y = tan-[ sec2(5x² + 1) csc-3 (cos 3x)]. Find

A:

Q: 1 dx 6- cos²xsin²x

A: use trigonometric identity to prove the integral

Q: d Find of tollowing functions. faa)= sin" (3%) "(3*) + loga (3²+2X-4)

A: Given: f(x)=sin-13x+log232+2x-4 we have to find the derivative of the given function. Use The Chain…

Q: (seč lix) dx

A:

Q: cos xdx 54-sin²x

A:

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: