(1 — х")dx

Q: dx 1+cosx 2.

A:

Q: Find the derivative. d. (In (9x? + 4)) dx di (In (9x? + 4)) =| dx

A: Solution:To find:ddx ln (9x2+4)=?Formula:ddx(log x)=1xddx(xn)=nxn-1

Q: e sinh 2x dx

A: The given integral,       ∫e-xsinh(2x) dx

Q: e cos x dx 01

A: To find:∫0∞e-x cosx dx I=∫e-x cosx dx…

Q: vi. ſ cos(3 Inx)dx

A: Using definite integrals,

Q: Evaluate d/dx sin^3(e^x) + 10^100.

A: Given:

Q: 11. Find e*sinx dx

A:

Q: d rarcsin(x) dx

A: Given that; ddxarcsin(x)

Q: S cos32x dx.

A:

Q: Evaluate fea cos(2x) dx

A: We have to above integration

Q: 2. e* sin x dx

A: (2). We need to evaluate the following integral  ∫0πexsinxdx

Q: S se ex dx

A: LetI=∫sec3(x)dxI=∫sec2(x)sec(x)dxApply integraion by…

Q: S cos(2x)e2x dx

A: We need to evaluate: ∫cos(2x)e2xdx

Q: 4. Find an approximate value for fo In 1+x³| dx.

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: sinh? 2x dx 3sinh? 2xdx

A: Given ∫-3 sinh3(2x) dx ⇒∫-3 sinh3(2x) dx⇒-3∫sinh3(2x) dx Now solving ∫sinh3(2x) dx substitute…

Q: 14. S4 cos (-3x + 2) dx

A:

Q: e Cos xdx

A:

Q: 5. Sx? cos 6x3 dx %3D

A: We have to evaluate the given integral by using theorems of antidifferentiation.

Q: 2. I cosh ix dx

A: The given integral is ∫cos14xdx. Evaluate the integral.

Q: 2TT Sin nx dx

A:

Q: d dx sinh(Vx)=

A:

Q: 13h dn.

A:

Q: dx A. 1+cosx

A:

Q: S cos 2x dx COSX

A:

Q: S tan 2x dx

A: Consider the given integration. I=∫tan2x dx Use trigonometric identity. tan2x=sin2xcos2x So,…

Q: So Si S*x 1 су-х ху dzdydx

A: Let the integral be  I = ∫01∫x1∫0y-xxydzdydx 'I' can be solved directly by integrating individual…

Q: So cos(Anx) dx on lo0) (0,00)

A:

Q: S cos(7x) cos (18x)dx

A:

Q: S Arctan2x dx

A: This is to be solved by the technique called integration by parts

Q: If y = sin x – ln (2x), then dx3 ||

A: The given function is: y=sin(x)-ln(2x)

Q: a) | x In ædx

A:

Q: In(1 – x) dx

A: We have to solve this integration

Q: 1/4 S (2 + sec)? dx

A: Please go through the attached solution. I hope that it  will help you .Thankyou . Best regards.

Q: dx =0 cos(x³) A) True False B

A:

Q: dx 10) T vin @cos Odo or Ode COS 77/3

A:

Q: if x = acos30, y = asin30 , find /1 + 2 dx

A:

Q: dx 1+cosx

A: Here we have to evaluate the given integration.

Q: dy 5. х dx - (1 + х)у %— ху?

A: The methods and formulas to find the solution of the Bernoulli equation help to find the required…

Q: (iv) ſeax cos bx dx

A:

Q: S cos²(2x)dx

A:

Q: find dy/dn in5 フx 34+2

A: Since you have posted multiple question We solve only first question  for reaming question post…

Q: 5. Sxcot°(10x²)dx 6. S ( tan (3z) dz cos*(3z)

A:

Q: Kindly sotve por : Dx (In | v | ) = Dx ((tan (3x) - In | 2x| + ( x³ - In | e|) - In | Inx | )

A: On differentiating Lhs: ddx(ln y)=1y.dydx on differentiating Rhs: ddx( tan(3x).ln|2x| +…

Q: fx cos 2x dx

A: Let's solve given integration.

Q: d d re' dx 'In x

A: To evaluate: ddxexlnx We know that ddxex=ex and ddxlnx=1x Quotient rule of differentiation states…

Q: In (x) -dx is equal to x2 The numerical value of

A: Given is an integration and we have to find it's numerical value. Here, we use the Integration by…

Q: S tan-Vx dx =

A: Using substitution and formula of integration by part.

Q: eMx cos nx dx

A:

Q: 19. S.cosTa de cos7x dx 5

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: