sin *x· cosx dx

Q: √√x-³√x+3x-1 dx 1. S

A: The calculation follows as:

Q: Integrals Evaluate each integral.

A: Given: evaluate.

Q: Evaluate the integral of cos?ydy

A:

Q: | sin³y dy ,3.

A: Given: ∫0π3sin3ydy

Q: x² dx √1+4x³

A: Solution of given question is written in below steps.

Q: Integrating Polynomial Functions integral  sin x/  cos^2   x     dx

A:

Q: (v sin?v dv

A: we have to use integration by parts to evaluate the given integral. ∫vsin2vdv

Q: 5) S dy 5.)

A: The given integral,      ∫28-y2dy

Q: Separation of Variable (cos'x-sin x+ sin' xkx + sin x sin y(1- sin x)dy = 0

A: Separation of variables

Q: 2 sin°x · cos' x dx

A: The given integral is I=∫0π2sin9xcos7xdx, rewrite the integral to get:…

Q: .J (6xy*) dy dx (бху?,

A:

Q: 1. tan 30d0

A:

Q: In 2 e2x dx /1 + e*

A: power rule: ∫undu=un+1n+1 Use basic rules of integration to solve the problem.

Q: 2 sin°x · cos7x dx

A: The given integral is  I=∫0π2sin9x cos7x dx It can be rewritten as I=∫0π2sin9x cos2x3 cosx dx Now…

Q: 1 dx V1-x

A: We can find the integration as below.

Q: Different methods x2 -dx using the substitution u = x + 1. x + 1 a. Evaluate b. Evaluate - - dx…

A: Integral ∫x2x+1dx a) Evaluate the using the substitution u=x+1 Take, u=x+1 du=dx so,…

Q: Integration techniques Use the methods introduced evaluate the following integrals. ∫x tan-1 7x dx

A: Evaluate: ∫xtan-1(7x)dx

Q: X + |

A: topic - indefinite integral

Q: 3. Vsin x+1 cos.xdx

A: Solution

Q: S Vex – 9 dx

A: Given integral is: I=∫ex-9dx Let us consider, ex-9=u2ex=u2+9exdx=2ududx=2uexdudx=2uduu2+9

Q: dx V1 + 8x

A:

Q: dx 5 (a²+x²)7

A: To integrate ∫dxa2+x252 using substitution method. Solution: Let substitute x=a tant.…

Q: |(x-3-8) Evaluate the integral dx using the Fundamental Theorem of Calculus. 1/2

A:

Q: t' sin(2t*) dt

A: given,       ∫t7sin2t4dt

Q: Arcsin y dy

A: Let us find the value of ∫01Arcsiny dy. This can also be written as ∫01sin-1y dy Let I=∫01sin-1y dy…

Q: sin'x Evaluate the integral dx sin'x+cos°x

A:

Q: EQUATIONS REDUCIBLE TO EXACT EQUATIONS RULE 1   (sin y + ysinx)dx - (cos x - xcos y)dy = 0

A: sin y + ysinx)dx - (cos x - xcos y)dy = 0

Q: 3 sine Q.4 Evaluate the following integral : de cos -sin?- | 2 2

A:

Q: 2 хcos 2x dx

A: To evaluate the integral: ∫0π2xcos2xdx Solution: Integration by parts states that: ∫uv dx=u∫v…

Q: 1 dx dy (2x + 3y)²

A: Given that, the integral I=∫12∫01 12x+3y2 dx dy

Q: Printegrating Factors (x² - Sin²y) dx + x sin zydy = o

A:

Q: dx 1+Vx

A: Use the appropriate substitution and than simplify the expression in standard form to integrate…

Q: 5. x+2 (x²+4x-3)5 dx

A: This question is based on indefinite integral.

Q: ,3 dx (x2+а2)3

A: Given integral is: A=∫x3(x2+a2)3dx                   (1) Use substitution method to solve this…

Q: | sin'y cos*y dy 프2

A:

Q: 5. S de x In x

A:

Q: lim 0 2 + sin(okr }) k=1 6 O A. J(x + sin(2xx)) dx 6 O B. J(2x + sin(2xx)) dx 3 O C. J(x +…

A: Definite integration limit as sum

Q: 1 dx 2 Jo (x-1)²

A:

Q: (sinh4dx 11. cosh2x

A: According to our company's guidelines I can only answer first question since you have asked multiple…

Q: (2) Evaluate the definite integral ₂ |x|dx.

A: Concept: Definite integral: The region beneath a curve between two set limits is a definite…

Q: dx а. x V4+ln?x

A:

Q: Definite Integrals Q: 1+ sin x

A:

Q: Scosx(bin x – sin’ x)&x. cos x(sin x – sin³x)dx. Evaluate

A:

Q: dy 1.5: ey sin( e-y)

A: To evaluate the given integral: I=∫dyeysin(e-y)

Q: S sec20 · tano(1+ 3tane)ž do

A: To determine the indefinite integral.

Q: Line integral (Calculus 3) #1

A: As per the company policy i can answer only first question for you,more than that leads me towards…

Q: sin 0 d) lime tan 0 sin z-cos z + 1 e) lim, 0 3z

A:

Q: dx х? V4 — х2

A: