75. dx -(coth x) = - csch? x

Q: S. S. dy dx

A:

Q: 1. ſ ev¤dx

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Evaluate the integrals in Exercises

A: ∫-ln20cosh2x2dx∫0ln104sinh2x2dx

Q: S cFinz (Inz + 1)dz

A: Given: 7. ∫azlnzlnz+1dz To Find: To evaluate the given integration.

Q: -п/8 S sec? (2x)dx

A: We have to evaluate the definite integral: ∫0π8sec22xdx Assuming, t=2x Then definite limit will also…

Q: Ex Evaluote S 4e sinhx..dx

A:

Q: Calculate the deriv L tan2tdt d_ dx II

A: Derivation of          is calculated as shown below

Q: d VE evedt dx d -S Intdt dx 1

A:

Q: 57. Verify that S2 yields the exact value of | (x – x³) dx.

A:

Q: Compute the exact value. 2 dx 2.

A: Simplify the given integral using limits.

Q: What is ſ e2x dx? 1+ex

A: Given :                      ∫e2x1+ex dx     Substitute u = ex+1  ,  dudx = ex…

Q: (3) SaʼIn a dx =

A:

Q: S se ex dx

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

Q: 1 en (enx)+ dx (enx)?

A:

Q: dy 2ху 3 Зу*, у(1) %— dx 112

A:

Q: iii. Sx coth-x dx.

A: (III) Apply the integral by parts rule, ∫u.vdx=u∫vdx-∫dudx.∫vdxdx Here, u = x and v=coth-1(x) As we…

Q: 22. Evaluate So Si S dx dy dz.

A:

Q: Sxe* dx

A: As per the guidelines when multiple question are posted in single pic  then we are supposed to solve…

Q: S tanx It Cosuy dx

A: Topic:- application of integration

Q: Evaluate

A:

Q: evaluate Fhe In tegral 子 dx

A:

Q: 5 dx, correct +2x²) Problem 19. Evaluate (3 to 4 decimal places

A: ∫0152x2+3dxSubstitute u=2x3→dudx=23→dx=32du=∫532(3u2+3)duSimplify:=523∫1u2+1duWe know that…

Q: 11. Evaluate dx if possible. If not possible, explain why. Vx? – 9

A: The objective is to evaluate the integration.

Q: Find y' if y=In(tanhx) +cosh¬1(coth2x)

A:

Q: 12. Evaluate /(ex)² dx

A: We have to evaluate the integral.

Q: find dy /dx for Hhe followiny (इस्ट '5र) +4 (In 2X) te

A: Given : y = 3ln2x+ecscx2+4sec-15x

Q: L{ e¬at sinh wt} =

A:

Q: d Verify coth x = - csch² x. dx

A: Differentiation is the rate of change of some variable with respect to the other variable. If a…

Q: 13h dn.

A:

Q: If x = a cost + log tan- y = asint 2 Find dy/dx

A:

Q: d tanh (u) du Sech (u) dx dx

A:

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: (e) S, In|x| dx.

A:

Q: 2) у(и? + 1)du + (из — Зи)dy — 0 -

A:

Q: too e dy

A:

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

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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: 2. S csc²¹ 5x cot¹ 5x dx

A:

Q: What is wrong with this calculation? 1 dx In |x||, = In 1 - In 1 = 0 - 1

A: The integral of 1xwith respect to x is log(|x|). where x≠0, cause if it is zero then function became…

Q: Find de when y = In(1+ 5/æ) dx

A: The objective is to find derivative.

Q: 10. S sinh rai tanhxainhr-tenha -dx

A:

Q: 16 Evaluate ſ," x²In 3x dx correct to three decimal places.

A: Given- ∫12x2ln3x To find- The value of the above integral. Concept Used- The above integral can be…

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: 7 dx = x3

A: ∫xndx=xn+1n+1+C1xn=x-n

Q: S(sech²(cosh3Ø)sinhø dø

A: According to question given :∫(sech2cosh3ϕsinhϕ dϕ

Q: dy y(ln y – In a + 1) dx 1 C = -ln C = -In Option 4 O option 2 1 C =-In

A: This question is based on solution of differential equation.

Q: 19. S.cosTa de cos7x dx 5

A:

Q: Sy sinh dy a

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.