dx 1. 1 = - X- (a) Show that the substitution x = 3 sin e transforms I into (b) Evaluate I in terms of x. de, and evaluate I in terms of 0.

Q: 4. e2x sin e*d x, use algebraic substitution

A: Given :  Intergral ( e2x sinex dx)

Q: dx dx Solve the equation +3 + 2x = e' given that x (0) = 0, x' (0) = dt

A:

Q: cos(x)In(1 + x²) + æ4.8 dx. Evaluate 1+ el.69z – 42.8 answer =

A:

Q: Use this equation to find  dy/dx. 5y cos(x) = x2 + y2

A: Given:

Q: 6. dx dy + cos.

A: Given: dydx=yx+cosy-xx

Q: Evaluate: - / (e* -e*)dx e ¯X+C 2 A | B) None cosh x +C 1 - sinh x +C 2 D E sinh x +C F -cosh x + C…

A:

Q: (cos 12/1- x2 1 1. Evaluate dx by using appropriate substitution. an

A: Evaluate ∫01cos-1x2121-x2dx

Q: T/2 e2x sin x dx

A:

Q: Consider the implicit function. e = sin (4x) dy in terms of x. dx Determine the formula for dy dx

A:

Q: (D2 -3D+2) y = e sin (e") - 2

A:

Q: df (x) If f(x)= log,s 2 cos 4.x|+ sin x|, Then find 9 dx at x = - 6. -

A: Given, f(x)=logsec2ccos4x+sinxTo finddf(x)dx at x=-π6

Q: tanr sec r dx 3

A: Here we will find the antidarive.

Q: -2 e* sin(x) -dx 1+ x2

A: the solution is as follow we will solve the given problem by numerical method  Trapezoidal rule

Q: COS πx dx S1n, πx

A:

Q: y cos x- sint x %3D

A: Given: Y = cos4x -sin4x

Q: L(cos at) = s2 - a2

A: To verify that ℒcos at=ss2-a2.

Q: dx (2) 3y sin x - -2xy cos x = 0 dy

A: Follow the procedure given below.

Q: dx. (a) [ cosʻ x+4 sin x (i) Evaluate Using the substitution ttanx

A:

Q: e cos-1x 5. S V1-x2 dx

A: To evaluate the given integral.

Q: sinh(Inx)dx 1) 2) fe* sinade e*.sinxdx 3) sin? (2x).cos(3x) G

A:

Q: 4. Solve for ſ e* sin x dx in the equation S e* sin x dx = e* sin x + e* cos x - Se* sin x dx + c.

A:

Q: I= ( cos(In(x)) dx 13- I =

A: GIven that: I=∫cos(ln(x))xdx

Q: 3) f₁ dx do - cos 0

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: (a) L{t+ sin 4t – e cosh nt} -

A: As per our guidelines, we are supposed to solve only first question.

Q: (a) Find dy for dx = In (3x – 2) (tan 2x) -

A: Explanation of the solution is given below..

Q: By using the substitution u = x3", find nx3n-1e + 8) dx where n is a constant. Hence, evaluate "(exn…

A:

Q: – 2x 4. Find the first five derivatives of y = Sin 3x+ e¯2x + In 7x. %3D

A: Our Aim is to calculate the first five derivative of function given below:-y= sin(3x)+e-2x+ln(7x)…

Q: Find dy/dx of the equation y=ln(sinx) when x=pi/4 a. 3 b. 1 c. 0 d. 2

A:

Q: dx 27 (d) 2 + cos (x)

A: As per bartleby guidelines we are supported to answer only one question at a time . Kindly repost…

Q: The antiderivative of Cos(3x)

A:

Q: 3. Solve the ODE using Separation of Variables. y². dy = (y² +1) - sin x dx

A:

Q: 2 dx (a) t = tan x. %3D 5+4 cos 2x 0.

A:

Q: Solve the equation for x .   a)ln(1 + e-x ) = 3       b)sin x = 0.3

A: we have to solve for x in the equations        ln(1+e-x)=31+e-x=e3…

Q: Find e-t sin(v3t) (a) L dt (b) L-1 -1 tan

A:

Q: (d) ƒ COS √1+sin x dx, (e) cos(lnx) S dx Т

A:

Q: 16 ) d du -1 cos и — 1<и<1 dx V1 – u² dx

A: As we know that the differentiation properties:- chain rule: ddx(f(g(x)))=f'(g(x))g'(x)…

Q: (a) [In(4) - 2e¹³] dx d b) dx d (c) [2²² - 1 (2²)] = 4e³x In(x [sec (12r) + tan-¹(2x)]

A: NOTE: Refresh your page if you can't see any equations. .

Q: 2T d) f(x)=5 sin (x+1)+2 e) f(x) = -2 cos 2(x+ 1) + 1_ 17. Find the rule of the sinusoi

A:

Q: Solve the equation (1 + x cosy) dx - x²siny dy = 0 using substitution.

A:

Q: e* sin(x)dx 3. Evaluate

A: We have to find the integral of given function

Q: Integrate x cos(2x^2+7) dx. Select the correct response: O sin (2x^2+ 7) + C

A: Integrate using substitution method.

Q: dx +x cos(t)-sin(2x) = 0, dt sin(2.x)

A: We have to slove this ODE:

Q: QI: Solve the following DE: e*dx-ydy 0y(0) = 1

A:

Q: (ei-e) dx +x cosh udu = 0 when x = 0; u = 0 1. %3D

A:

Q: Find dy/dx of: x3 - sin y = (1/x3) + tan-1 (ey) - π/4 Don't simplify the final answer.

A: Given:     To determine:

Q: Q1-Find S sin 3x e4* dx

A: let I=∫sin3x e4xdx using by parts I=e4x∫sin3x-∫ddxe4x∫sin3xdxdx simplify I=e4x∫sin3x-∫12e4xcos3xdx…

Q: Solve for the differential of y when y= sinxx, x=-, and dx=-. 3 2 A B D

A: In this question we have to solve the differential of y.

Q: dx It sin x-cos x COS

A: To evaluate:∫dx1+sinx-cosx Solution: We know,cos2x=1-tan2x1+tan2x     ...(1)sin2x=2tanx1+tan2x…

Q: dx 3+2 cos x

A: The value of the given integral is 2√5/5 Arctan[√5/5 tan(1/2 x)] + c

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.