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

Q: What is the (2sec?x – sinx) dx O sinx + 2tanx + c O 2 sinx + cosx + c O cotx + 2 cosx + c O 2 tanx +…

A: The given integral is: ∫2sec2x-sin xdx

Q: Use the accompanying figure to show that 7/2 sin x dx sin 'x dx. 2 y = sinx 1 y= sin x 1

A: Given: To prove, The given graph is shown below,

Q: 27. What is the simplest form of sin 2 tan'x A) 1+x B) 21+x? 2x C) 1+x 2x D) |1+x?

A:

Q: Using appropriate substitution, S [sec³ (2x) – 2] tan(2x) dx is equal to

A: integration

Q: Evaluate Sz cos“ x sin? x dx

A:

Q: Q.2: Evaluate: cos³ x I = = =dx sinx Hint: Sin’x+ Cos'x =1

A:

Q: Evaluate fe'(si Je*(sin x +cos x)dx

A:

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

A:

Q: The general solution of y 'tanx sin2y = sin?x + sin?y is

A:

Q: Use the substitution rule and show all the steps to evaluate: 1 dx 1+ sin x – cos x

A: ∫π3π2 11+sinx-cosx dx Apply u substitution u=tanx2 find derivative of u with respect to x…

Q: Using the substitution u = sin (x), or otherwise, find the exact value of %3D J sin° (x) cos (x) dx.…

A:

Q: 44. Use the accompanying figure to show that sin-x dx. sin x dx y = sin y = sin x

A:

Q: coso dz+ (2Z o)do= o sin © - Cos

A: Use exactness formula to check and then solve

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

A:

Q: d (cos x) H.W.: show that -sin x %3D xp

A: Given: To show ddx(cos x)= -sin x Definition : Derivative of f(x) w.r.t. x is defined as:…

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

A: Given: ∫cos2xsin4xdx

Q: Using appropriate substitution, f sin°(x)cos³ (x)dx is equal to:

A:

Q: Use the method of substitution to evaluate | 2x cos x? dx.

A:

Q: Evaluate 1 dx 3 sin x – 4 cos x -

A:

Q: Let f(æ) = - 6 sin(x)cos(x). %3D df dx d²f da?

A: Using product rule, (uv)'= u'v + v'u Here we take, u = sinx v = cosx df/dx =(uv)'…

Q: 3. Are reduction formulas needed to evaluate sin x cos? x dx? Why or why not?

A:

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: Using the substitution u = cos(2x), S sin (2x) cos (2x) dx %3D

A: The given integral is ∫sin52xcos32xdx.

Q: a) ㅠ 3 cos x sinx dx

A:

Q: Verify the identity. sin(x + y) – sin (x - y) = 2cos.xsiny

A: To verify the identity, sinx+y-sinx-y=2cosxsiny

Q: Given that sin(x)dx = 2, find I = 3 sin(x +2 7)dx. ||

A: Given that: ∫0πsin(x) dx=2 To find I=∫05π3 sin(x+2π) dx

Q: 8. Evaluate sin (x) cos(r)dr using an appropriate substitution.

A: here  we use the formula  ∫(xn)dx=xn+1n+1+C     according to our guidelines we can answer only…

Q: Show that the two formulas are equivalent                                                      ∫tan…

A: To show that ∫tanx dx=-lncosx+C and ∫tanx dx=lnsecx+C both formula are equivalent. We know that…

Q: Evaluate o (3 sin x – 5 cos x) dx.

A:

Q: Evaluate | sin X cos X dx 3

A:

Q: 2 sin (x) dz 4 cos? (x) + 2 cos (x)

A: The given integral is ∫-2sinx4cos2x+2cosxdx. Determine the value of integral by using partial…

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

A: Given integral is We will evaluate the integral by substitution method.

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

A:

Q: 7/2 sin 7x cos 5.x dx JO

A: Recall: 2 sin(A)cos(B)= sin(A+B)+sin(A-B) ∫sinax dx=-cos(ax)a+C

Q: Find y' , for y=Sin-1(Cos√x)+Cos-1(Sin√x)

A: The solution for the above question is as shown below.

Q: ( esch(3 tan z) + sin². 1. cos? r

A:

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

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

Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

A:

Q: Evaluate sin (x) cos(r)dx using an appropriate substitution.

A: Given that, I=∫absin5(x) cos(x) dx We have to find the solution of above integration.

Q: Write the expression as an algebraic expression in x for x &gt; 0.

A: Given: secsin−1xx2+4

Q: Is this: sin x cos y- cos x sin y/ cos x sin y reciprocal quotient pythagoreom  algebra

A:

Q: Evaluate sin (x) cos“(x) dx.

A: ∫ππsin6x cos4x dx

Q: Use the double-angle formula cos 2x = 2 cos x – 1 to evaluate the integral 1 1+ cos 2x dx

A: The given integral is ∫11+cos2xdx

Q: Differentiate (sin(ax+b)/cos(cx+d))

A:

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.