Use the method of substitution to evaluate 2x cos x2 dx. sin x? + c 2 - sin x? + c sin x? + c - sin x? + c

Q: sin xdx 3. S 7+cos? x

A: Given integral, ∫sinx dx7+cos2x

Q: Rewrite – 2 sin(r) + 3 cos(x) as A sin(z + o) A = $ =

A:

Q: a) cosx = - ja 0 <x< 360° b) sin (2x +) = 0, ja - << c) 2cos?x + sin +x) – 1 = 0, ja 0 <x<2=

A:

Q: Use the method of substitution to evaluate 2x sin x? + c 2 sin x? + c sin x? + c 2 – sin x² + c

A: As we know that the common integration of : ∫cosudu=sinu ∫a·fxdx=a·∫fxdx

Q: Evaluate S2 sin? x cos3 x dx

A:

Q: sin x =dx V6 cos x – cos? x – 2

A:

Q: Find x where 0 <x < T. 2 cos?x = 1 Enter the smaller answer first.

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Q: |16 sin?x cos?x dx

A:

Q: state what method applies and how one applies it, but do not evaluate the integral:

A:

Q: Use the method of substitution to evaluate 2x cos x2 dx. sin x + c – sinx² + c - sin x? + c sin x?…

A: Solve by substitution method

Q: 23. x? sin (x³) cos (x³) dx

A: ∫x2sin5x3cos3x3dx=∫sin5x3cos3x3dx      x3=u,3x2dx=dx, x2dx=1/3 dx=∫sin5x3cos313dx

Q: Using an appropriate substitution, ſ sinº(x)cos³(x)dx is equal to: 10 coslx cos°x sin°x sinx + C 9.…

A:

Q: sin x (cos x + 4) dx 1+cos?x

A: Solution:

Q: W (1, sin x, cos x) =

A: Use formula for the wronskian is determinent form.

Q: Using (11) and (12): 1 dx 1+ cos x tan +c

A:

Q: Evaluate: sin rv1- 4 cos² x dx. /9 – (In r)² Evaluate: dr.

A:

Q: An equivalent expression to sin(-x) is: Oa) - sin(-x) b) sin(x) Oc) - sin(x) d) cos(x)

A:

Q: Evaluate: * cos² 2. * x cos? x dx sin

A: Given: ∫cos2xsin4xdx

Q: Evaluate (2 sin? x cos3 x dx 0.

A: The given integral,     ∫0π2sin2x cos3x dx

Q: Evaluate sin2(x) cos*(x) xdx 32 C. 32 A. 32 в. D. 32 O A В

A:

Q: How would you evaluate f cos?x sin x dx?

A: We need to evaluate, ∫cos2xsin3xdx

Q: Rewrite 1 sin(x)+ 2 cos(x) as A sin(x + 4) %3D Note: o should be in the interval-T <¢ < II

A:

Q: Rewrite – 4 sin(x) – 5 cos(x) as A sin(x + ø) A = $ =

A: Given the trigonometry function

Q: Evaluate va 3 cos a sin x dx. + C

A: To find: The value of integral ∫cosxsin3xdx. Formula used: The trigonometric relation is…

Q: Which identity is most useful in evaluating cos x dx ? cos 2x 1 2 sin? a %3D | COS T sin a - 1 O…

A:

Q: Evaluate o (3 sin x – 5 cos x) dx.

A:

Q: r sin ³0 cos³ 8 do 3

A: Topic:- application of integration and trigonometry

Q: dx 4. Evaluate cos? ' x (tan x + 1)

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Q: Express the given quantity in terms of sin x or cos x. sin (6t – x) O A. cosx- sin x O B. - sinx C.…

A: The given expression sin6π-x

Q: Evaluate sin(x) · In ( cos(x)) dx using substitution.

A:

Q: sin x (cos x + 4) dx 1+cos?x

A:

Q: sin' x -du u cos x =-[u-3u²+3-u' du

A: ∫sin7xcos4xdx We have to find the above integral.

Q: Find ?f if ?″(?)=2+cos(?),?(0)=1,?(?/2)=−8.f″(x)=2+cos⁡(x),f(0)=1,f(π/2)=−8. ?(?)=

A: To find- f(x)

Q: What is the value of x? √2 cosx-1=0 2sin3x+1=0

A:

Q: sin? x cos“ x dx. 4

A: We have to find integration of sin²x.cos⁴x

Q: Complete the identity. sin x COS X =? sin x COS X O A. sec XCSC X O B. sin xtan x O C. - 2tan x 2.…

A:

Q: Evaluate sin z -dx /4 - coS I

A: Use the substitution method and first simplify the integration than integrate.

Q: tinuous, prove that T/2 T/2 f(cos x) dx = f(sin x) dx (b) Use part (a) to evaluate /2 cos?x dx and…

A:

Q: Evaluate sin' x cos x dæ. x dx. Answer:

A:

Q: b. sin? () = 2 over [0, 2n) %3D

A: EXPLANATION

Q: e cos(x) = 1 + sin(xy) 2 2

A:

Q: (4x-) What is Y*? 2 Let Y = cos ( 4X

A: Step 1: Consider the given function:

Q: Substitute the expressions for u and for du to write tan(5x + 8)dx in terms of u. / tan(5x + 8)dx =…

A:

Q: cos x sin'x dx can be evaluated by factoring sin'x as (sin?x)²sinx and transform sin?x into 1– cos²x…

A:

Q: Evaluate f sin?cos xdx 13. Asin? +C c. sin? x cos³ x + C D.(ns cos2) + C ´sin³x cos x' B.를 sin3 즐 +…

A: ∫sin2x2cosx dx

Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.