1 4.) dx 36 22 5.) 10x d.x VI-

Q: dx = [Af(x) – B In(g(x))% + D S and if A =.B < 0 , then ƒ 2 dx = x+2 x+2 ...

A: The given integration: ∫abx2+x+12x2+2+x3+x dx=Af(x)-Bln(g(x))ab+D∫abdxx+2  →  eqn 1 From the above…

Q: F ind So S. eu dy dx.

A: Use the concept of reversing the order of integration. While integrating with respect to one…

Q: 12 Find p, q if f" f(x) dx – f' f(x) dx = S, f(x) dx. %3D (Give your answers as whole or exact…

A: Definite integral: - The value of a definite integral is known. For a function f(x) defined with…

Q: 5) Find if y = (cos h x)* dx

A:

Q: 3 Given that 3. e dx = e° - e, use this result to evaluate 3ex + 4 dx.

A:

Q: If z=5x^2+y^2 and (x,y) changes from (1,2) to (1.05,2.1), compare the values of delta z and dz.

A: Given that        z=5x2+y2 changes from (1,2) to (1.05,2.1)  We have to derive value of Δz and dz .…

Q: 2. J Зу /7—Зу?dy

A:

Q: (3) SaʼIn a dx =

A:

Q: 4 2 To find the blue shaded area above, we would calculate: b. f(x)dx = area a

A:

Q: の1) (のの) (めみ) Cn %3D Cnt = %3D antt San So,itis increa Sing. @dn=

A: dn=n32n! On simplification, we get dn=n32n·2n-1!=n22·2n-1! Now,…

Q: 3. Determine the complete solution using MVP: - cot(2:) dx

A: Given the differential equation

Q: 45. у 3D VI + * dt

A:

Q: π 2 EK 4 cot4 x dx

A: Here, note that: ∫cot4x dx=∫cot2x cot2x dx=∫(cosec2x-1) cot2x dx=∫cosec2x cot2x dx-∫cot2x…

Q: 2. I cosh ix dx

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

Q: In x²/25+ x² dx , we let x=5sine. A True

A:

Q: 2. cot2 x dx

A: Given- ∫cot2x dx To Find- The value of the above integral. Formula Used- cosec2θ=1+cot2θ

Q: Q.43) 2n S Icosx – sinx|dx =

A: Here we have to find solution of given integral

Q: 2. [ xsec’x cot xdx tamol svode se gniau s 3. ftsin2t dt

A: Disclaimer: “Since you have asked multiple questions, we will solve the first question for you. If…

Q: 1+cosx, dr r = 1-cosx' dx

A: Using derivative to find dr/dx

Q: 7) sinh 2xdx 8) fcosh vdv 9) f cot ydy pai4 sec? Jwdw

A:

Q: tan st dt \+9t?

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: ∫ 7 to 9 (4+3x)dx=

A: Given integral is,

Q: Hence, the work done is equal to the following. 5/4 W = 20/3x dx

A:

Q: zoom in 28 Er m. 10 14 X+7 28 co sh tw 14x = 28(x+ 7) 14x - 28x + 196 -196 = 14x -14 = x 3. II

A: Simplification

Q: 3. Find 4. Find 5. Determine -dx

A:

Q: dy _ 1 dx y-x 6.

A: 6) Given:             dydx=1y-x               dxdy=y-x                dxdy+x=y This is in the form…

Q: ,2x Set* sin(e2*)dx

A:

Q: 1/2 yee? +4 dy +17y=0 dx2 when Pove then ydy that Sinzx, %3D0 dx

A:

Q: 1. dy = %3D COSX cotytanx Cosy dr

A: Given- dy=1cotytanx-cosxcosydx To solve the given differential equation. Here we will arrange the…

Q: 13 12 dn use ful Ja?_36 Substitution x=6 Seco and rewn'te tue im tegrel

A:

Q: 1 Stan(x?)dx+2 x² sec²(x³)dx = | tan(x2)dx +2 x2 sec2(x²)dx= 4. %3D 0. Select one: True False

A: The integral function is given

Q: If Mesin(2x) dx= eSin(2x) + C_then the M is equal to Blank 1 (use small letter, no spa

A:

Q: (x) %3D 5 sec x, [л, 2л]

A:

Q: 3 3 ex dx = e3 - e, use this result to evaluate Given that %3D 7ex + 6 dx.

A:

Q: 10 Find p, q if 5" f(x) dx + Sio f(x) dx = f(x) dx. r17 (Give your answers as whole or exact…

A: Recall: a property of integral ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx such that a≤c≤b

Q: Given that ƒ(1) = 5, ƒ′(1) = 4, g(1)= 2, and g′(1) = 3, find

A: Given- ƒ(1) = 5, ƒ′(1) = 4, g(1)= 2, and g′(1) = 3. To find- ddxfx·gxx=1 and ddxfxgxx=1  Identity…

Q: In x25+x dx , we let x= 5sine.

A: ∫  x225+x2dx

Q: 4. Describe in detail three separate ways to find /. Evaluate any two of these to show that they are…

A: I=∫x9-x2 dxUsing substitution method:u=9-x2du=-2x dxx dx=-du2=∫x9-x2  dx=∫-1u du2=-12∫duu=-12∫u-12…

Q: If * 1 y = 3u? + 2 and u = -, x = 1 then dx dy ||

A: If  y=3u2+2u=1x x=1 To find dydx

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

A:

Q: %3D 23DQ

A:

Q: 7 dx = x3

A: ∫xndx=xn+1n+1+C1xn=x-n

Q: 6 ven cos a = wh 15'

A: Use inverse trigonometric ratio

Q: Determine how large the number a has to be so that dx

A: Given that: ∫a∞1x2+1dx&lt;0.005

Q: (2) Scass sydj 3) $ ( x 2 = 10) 2 3 2 १) (क olx dx

A:

Q: d 53. cosh? (9 – 31) = –6 cosh(9 – 3t) sinh(9 – 3t) dt

A: Given derivative is ddtcosh29-3t.

Q: If y = Ju+2 and u = 4x - 2, then dy/ dx is

A:

Q: B) Find and It x sin 3z and y= tan 3z dx

A: x=sin23xy=tan 3xWe need to find dydx and d2ydx2.