| (cos(3x) sin(x) – sin(3x) sin(x)) dæ

Q: 1- Differentiate. a- Y= 2 e2+1 b- Y= -2 sin?x c- Y= 3sin2x - cos 4x d- tanv(1-x)

A:

Q: evaluate using the appropriate method or combination of methods.

A: Use 2sinA*cosB=sin(A+B)+sin(A-B) formula

Q: Given: y = x - sin(2x) Find: dy dx 0 - cos²x 2 ○ - sin² x 01+ cos²x O sin²2 X

A:

Q: Determine of y = cos(x) – V5a2 In x.

A: I have stated the used formulas in the solution.

Q: Can you help me step by step?

A: The given function is,

Q: V. Show that: 1. [(cosx-sin x)'dx = x+ cos 2x +C 2.

A:

Q: of (e² 2-X Sin (2y)

A: Given, f= e2-xsin-1(2y) To find, df/dy.

Q: The approximation of I = = co cos (x²+5) dx using simple Simpson's rule is:

A:

Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: 1 1 S [ sin(1+ y²)dydx= 1- cosl a. 2 cos 5

A:

Q: y f(x)sin2x + g(x)cos %3D x) =tan3x x)% sin3x %3D - r) =cos3r

A: Differential equation: y''+9y=tan (3x)The auxiliary equation is,m2+9=0m=±3iComplementary function…

Q: 1 Evaluate [ (x³ +cos(3x))dx 2

A: The given integral is ∫x3+12cos3xdx.

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: If y = √√1-x² sin¹¹x, prove that (1-x²)+xy=1-x². dx

A:

Q: coS x dx 6) 1 + 3 sin x A) In| 1+3 sin x|+C C - 를 In| 1 +3 sin x| +C

A: To evaluate ∫cosx1+3sinxdx

Q: 4. Evalaute cos(x) sin(x) dx

A: Given:

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: aluate 9/ sin(x) cos(x) dx by four methods.

A: Here we want to perform the given integral according to each of the methods mentioned.

Q: 3 O f sin 2x cos 2xdx 4)

A: we use substitution method

Q: dr 1- y = Inlog 2- y = (cos x)*Snx 3- у e (sinx

A:

Q: /2 2 cos x dx 1+ (sin x)² -n/2

A:

Q: ¥2/3 6. cos'x sin x dx 5.

A:

Q: Integrate with respect to x: sin(3r) b 2 cos(4x) cos²(2x) a

A:

Q: Find dy/dx for y = 3[(sin-(e-3x*))2

A: Given,          y=3sin-1e-3x22

Q: 2 sin 2x dx Tcost x + 4 cos² x – 2

A: We will answer the first question since exact one was not specified. Please resubmit the question…

Q: 2. 1- x2dx cos(x + 1) dx 3.

A:

Q: x* cos 3.xdx 2 fr' cos 3.xdx sin 3xsin 2.xdxr

A: Solving

Q: 2. Evaluate: S(cos x)(In sin x)dx A. sin x (1 – In sin x) + C C. sin x(In sin x – 1)

A:

Q: 1. Calculate the Integral sin x cos x dx

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

Q: find sin x cos? x dx 75. 76. sin 2x sin (cos 2x) dx er dx et + e* (e2x + e)² dx 77. 78. x + 1 e* + 1…

A:

Q: (2) If y = (sin-1(x))², prove that (1- x2)y" – xy' - 2 = 0.

A: here first we will derivative with respect to x then squaring both side and put value of the y then…

Q: V3 with 0 < x < 2n. 2 cos 2x cos x – sin 2x sin x - -

A:

Q: Cos 5x dx 3 +Sin 5x 1. 2. dx J16-9 (n x)²

A:

Q: 2- y = prove that (sin x) = cos x %3D dx

A: Topic:- derivatives

Q: 4. y = tan(x+ a), 5. y = Aex + Be2x, 6. y = A sin 3x + B cos 3x, ,where A and B are arbitrary…

A: According to bartleby guidelines when student ask multiple subpart question then expert must have to…

Q: For | cos 3x cos 4x dx :

A:

Q: 3 In(1+ V sin²x .limr→0 V1– cos x

A: Consider the given expression. limx→0ln1+sin2x31−cosx Put the limit in the expression.…

Q: 2 Given that: J2(x)=-, cos.x + sinx find J(x)

A:

Q: 4 sin' 2x cos 4x dx 4.

A:

Q: 1) If f(x)= tan(5x), find  f'(5)=??????

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 7. Integral cos x dx sin x

A: This question is related to integration, we will solve it using given information.

Q: Cos 4x b. .J dx,u=1+2 sin4x (1+2 sin 4 x )*

A:

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: 4. Evaluate sin (44°) + + COS (29°) using differentials. Refer to special triangles.

A:

Q: S sin x (1+ cos 2x)² dx

A: In some cases integrals can be converted to standard integrals using an appropriate substitution.…

Q: cos x -dx Compute the integral 1+(sin x)²

A: replace sinx=u cosxdx=du limits of u will be 0 to 1

Q: of y = In || dx 4 1-cos x 1. 1+cos x Find the

A:

Q: Show that Sx cos*x dx = (x² + x sin 2x +cos 2x) + c

A: Given: ∫xcos2x dx=14x2+xsin2x+12cos2x+C.

Q: e3x [7 sin 7x + 3 cos 7x] +C 58

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

Q: 9. (2 sin x – 3 cos x) dx • T/2 - T/2 -

A: We use Trigonometry table for final answer  and cos(-x) = cos(x)  sin(-x) = -sin(x)

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.