Prove,J w' Sin wx du %3D COSZ 2

Q: Find the solution to the differential equotion that Sotisies the quen inital condiion

A: The differential equation with initial condition is given as

Q: evaluate using Integration by Parts.

A:

Q: sec 3x tan² 3x dx

A:

Q: | sin(6y) sin(8y) dy.

A: we have to solve the integral

Q: Evaluate the integral. .5 3 cosh(t) dt 0.

A: Solution

Q: Assuming Cov(X, u) = 0 allows us to equate Exû to zero. True or False? Explain.

A: Solution

Q: find integral csc 3 u  sec u du

A:

Q: Evaluate the double integral sin(y' +1)dydx.

A: Use the change of order of integration to solve this problem.

Q: 4. Evaluate the integral. S tan (2x) sec°(2x) dx

A:

Q: Differentiate. cosx² + siny³ = 36 %3D

A:

Q: Evaluate the integral. 5 cosh(t) dt

A:

Q: Evaluate the integral f sin²(3x) cos (3x) dx.

A: The given integral is ∫sin23xcos53xdx. We have to evaluate the given integral.

Q: Prove that  d/dx[cosx]=-sinx

A: We will use the definition of the derivative  Here f(x)=cos(x) So,

Q: Prove that Va2 + 4 sin ( sec %3D V2 +4

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

Q: Find the of Integ ration f(u)= tanu + Cos 2u. %3D

A: Given information is :

Q: Evaluate the integral. 10 sec 2(5t) dt J7+2 tan (5t)

A: We have to integrate the  I=∫10 sec2(5t)7+2tan(5t)dt

Q: sec sec |tar xp xp Suea () 2asS

A: We put sec(π/x2)=u and differentiate both sides with respect to u .thus we get du and value of…

Q: Find the area.   y = 3 cos(4x),    y = 3 − 3 cos(4x),    0 ≤ x ≤ π/4

A:

Q: Calculate the integral (а) dx (*/3 Vtan 0 (b) п/4 -do sin 20

A: Given : (a)  ∫-∞∞x5e-x2 dx    (b) ∫π4π3tanθsin2θdθ

Q: find: de So 2-cose using sediment theorem

A: Solution :-

Q: Evaluate the integral 9t tan (1) dt

A:

Q: 3 4. sin x cos xdx

A: These formulae are used while solving the question:

Q: Integrate sin" uelor (cosu) . Where n=540

A:

Q: Evaluate the double integral [ Vy sin ydydx.

A: • Here, the inner integral w.r.t 'y' is difficult to evaluate, hence we have to change the order of…

Q: Compute this integral ∫ (xsin^2(x)cosx) dx

A: We use integration by parts

Q: sin x + 10(csc x)² dx

A: To compute: ∫(sin x+10(csc x)2)dx

Q: Prove d [sin-! lu(x))]= I dx dulx) %3D NI- Culx)]? dx

A:

Q: Use the tabular method to evaluate the integral |(* + 2x – 1) cos(4x)dx

A: Given:∫(x3+2x-1)cos(4x)dx

Q: Find an eqeation of the to the cune at the onuen povnt tangent line t 48) y=In(x²_ 7), (2,5)

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Q: Use Property 8 to estimate the value of the integral.

A:

Q: Use the results of Section 5.2 to compute the following definite integral: 4x2 dx %3D

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Q: Evaluate the integral + tan sec dt

A:

Q: cos'xsin*xdx IN

A:

Q: can this be evalnated by using L'HUSpital's Rule? im x2 3x+ 2 sin(x x)

A:

Q: sec? (4x)(3 – tan(4x))³dx

A: Given integral is,  ∫sec24x3-tan4x3dx. Substitute t=3-tan4x.…

Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

Q: 4. Use Trigonometric substitution method to evaluate the integral: dx

A:

Q: sec (7x)tan' (7х)dx

A:

Q: Evaluate the integral. integral   sec 6  t  / tan 3t dt

A:

Q: sec®3xtan3x dx

A:

Q: If y=tanx , prove that y```=2(y^2+1)(3y^2+1)

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Q: dt cos°(2 sin" 21)/1– 4r cos(2 sin2t

A:

Q: What is the integrable form of sin-cos-sine de? 2 2 V1-u? du -2 sinu du u² – 1 du 2/ cosu du

A: We have given integral Let, I=∫sinθ2cosθ2sinθdθ As, sin2x=2sinxcosx sinx=2sinx2cosx2 So,…

Q: Left in implicit form

A:

Q: Integrate by parts f(x)=sin4(x)cos3 (x) dx

A: Given the integral  I = ∫cos3(x) sin4(x) dx cos2(x)=1−sin2(x) I = =∫cos(x)(−sin4(x)(sin2(x)−1)) dx…

Q: 2 = sin5t constitute a fundamenta L

A: Y1=cos5t and y2=sin5t  do not a fundamental set of solutions of differential equations y"+16y=0

Q: Evaluate the double integral. 5 25- х2 dy dx Jo

A: First, integrate with respect to y

Q: Evaluate the integral: 7/20¹² sin (1) dt du

A: Follow the procedure given below.

Q: cos' x dx

A: