11. Use the substitution u = x/3 to prove dx tan 9+x2

Q: Find the indefinite integral ∫tan6 3x dx

A:

Q: sec 3x tan² 3x dx

A:

Q: Evaluate [/3 cos(x) In (sin(x)) dx T1/6

A:

Q: 11. Evaluate the integral: tan 2x dx A. -In| sec 21| + C -sec² 2x + C С. -In| cos 24| + C D. 2 sec…

A:

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

A:

Q: 5) Evaluate the integral: tan 3 x dx

A: Given integral, ∫tan3x dx

Q: Evaulate the intergral: ∫−10sec^2(x)tan(x)dx

A: Consider the given integral:

Q: 5. Evaluate dz (sin(x*)).

A:

Q: 5.Use trapezoidal rule to evaluate f,(x² + 1)7 dx by taking n = 4.

A:

Q: Prove that  d/dx[cosx]=-sinx

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

Q: S. 3 Estimate tan x dx using the midpoints of 6 rectangles.

A:

Q: d Prove that (sin-l x) : dx V1 – x²

A: To show that:ddx(sin-1x)=11-x2

Q: Find the indefinite integral ∫tan3 3x dx

A:

Q: Evaluate the integrals

A: We have to evaluate the integral;  13) ∫ln4ln9ex/2 dx14) ∫tanxln(cosx) dx

Q: リ=!-Cos2x 1+(os 2x prove y = 2 tanx .secx

A:

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

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

Q: .Find a reduction formula for ea* sin" x dx. Hence evaluate e* sin x dx. 3

A:

Q: Compute (6x7 + 1/x7 +cos x ) dx

A: We have to evaluate:

Q: 5. If y= tan x, prove that y``=2(1+ y² )(3+ y²).

A: Prove the given equation

Q: Evaluate (a) ſ In(2x + 2)dx /3 (b) [ sec'3x tan 3x dx

A: Please see the answer in step 2

Q: S tan (2x)sec (2x)dx = %3D

A:

Q: 1. If Y= 4 In (In (In(sec(x)) then Ý=[4 (tan)/{ In ((In (sec)) In (sex)}]

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Q: -sin (In x?)ecos² (In x) dx 100x2-x2e2 cos (In x)

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Q: d Prove that sin x cos x from first %3D dx principles only. Be sure to prove any limits that are…

A: Let's learn first principle of derivative because we have to find derivative of sinx using first…

Q: What substitution should be used to solve the integral S O sin u=3x/2 O sec u =2x/3 O sec u =3x/2 O…

A: Evaluate the integral by using substitution method

Q: Evaluate / 5 sec2 *dx tan(x) 05 In(|tan(x)|) + C Oln(tanx) + C 05 In(x) + C 05 tan(x) + C

A:

Q: 2- S tan x dx.

A: Given integral is: I=∫0πtan x dx We have to evaluate this integral.

Q: 3. S In(cos x) tan x dx

A:

Q: Evaluate. S sin“ x cos² x dx

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

Q: (§5.4, Q42) Calculate So™ f(x) dx, where sin x, x T

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Q: Solve using the false rule method f(x) = /x² + 1 – tan x %3D starting at the interval [0.5,1]

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Q: y = In (3²×) + sec (Inx²) + tan¬1(In5x)

A:

Q: 1. Evaluate 1 (a) [ In(2x + 2)dx (b) [ sec'3x tan 3x dx

A: (1)(a) Use the method of substitution to solve the definite integral.…

Q: 1. Evaluate 4 (sec²x tan²x ). dx

A: Use product rule of differentiation du·vdx=vdudx+udvdx. Use chain rule of differentiation…

Q: (22 – 2) | Evaluate dx 2+2 (x4+5x2 +4) tan1 2 A - BI E E E E X O Type here to search 马

A:

Q: (B) Evaluate tan (3.x +1) sec³(3x +1) dx

A: In this, We find the value of the given integral using tan^x+1=(sec^2)x formula.

Q: 33. Prove for a > 0: dx x2 + a 1 tan Ja

A:

Q: 1. Evaluate (sec²x tan²x ). dx

A: To find dsec2x tan2xdx Given function is y=sec2x tan2xwe know that, sec2x =1+tan2xthen…

Q: f(x) = cos (In (3x))

A:

Q: 3. Show that: • T/2 sin" x dx • T/2 cos" x dx

A: Recall the property of definite integral:

Q: 19. Evaluate using u-substitution: S tan6x sec² x dx

A:

Q: Compute / tan x · sec a dæ.

A: detailed solution is given below

Q: Evaluate integral 0 to pie sin 2 x cos 4 x dx

A: To Evaluate the integral given below:-I=∫0πsin2(x)cos4(x)dx

Q: Find 1-x if y = cos-l dx 1+x²

A:

Q: 1 Integrate: S tan*÷x dx 3

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Q: What is q'(x) when q(x)=ln((5x^2+x+7)/((x^2/3)(sin(x)))

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Q: 4. Use Secant method with p =1, p =1.2 to find the root of f(x)= Inx – cosx that is accurate to…

A: Given, fx=ln x-cos x; p0=1; p1=1.2; As it is known that the secant method is given as,…

Q: 3-Еxpand In [x' sin x /Vx2 + 1]

A: According to guidelines we should have been able to solve only one question at a time #3 expand

Q: Evaluate integral 0 to pie sin 2 x cos 3 x dx

A: Explanation: Given that,  ∫0πsin2xcos3xdx   Formula Used: Trig. identity:1-sin2x=cos2xSum rule of…

Q: Q4) Prove that dx 1+ 2 sinx || In √3 Χ tan tan x + 2 -√√3 +2 + √√3

A: