- In-2. Hence show that In = 01 tan" x dx = n - 1

Q: sin x dx cos5x b.

A:

Q: 8. Evaluate the integral. sin x xp. 4+ cos x

A:

Q: Q2/a) Find the integral f tan5x dx cos³x b) Find the integral cos*x dx 1-sinx

A:

Q: Find the indefinite integral (tan -1æ}? dx. 1+ x2

A:

Q: 00 -dx- ;, 0 < p <1. sin px 7. Show that 1+x

A:

Q: 1. Solve for x, where 0 < x < T. 1 tan x = sin(2x)

A:

Q: (a) Find dy/dx for 3 tan x – In x x2 (b) Find f"(x) for the following function: e" In(x**) f(x) = x…

A:

Q: Integrate the following. - sec²x 3. ( sec?x tanx

A:

Q: FIND DY/DX OF THE FOLLOWING 3. y-tan (1+sinx)

A:

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

A:

Q: Find a, b, and c for the function f(x) - a sin(bx- c) such that the graph of matches the figure. (x)…

A: Given  the given form of the function is fx=asinbx-c and the graph is

Q: S tan ( – y) dy 4

A: ∫tany4-y dy=∫tany-4y4 dy=∫tan-3y4 dy Now put, -3y4=t⇒-341=dtdy⇒dy=-43dt

Q: use this to evaluate /x*sin (2x)dx

A: Integrating using by parts...

Q: y = 7 tan x, for x in 2'2

A:

Q: d/dx [tan-1(tanx)]=1 for all x in the domain. True or False?

A: Given statement d/dx [tan -1(tanx)] =1 for all x in the domain. is true.

Q: (3) Estimate the error involved in using the approximation cos x = 1- for |x| < 0.01

A: To estimate the error involved in using the approximation cosx≈1-x22 for x≤0.01 The Taylor series…

Q: Find y'. Given: y = -cos(4x)tan(4x)

A: Solving the problem by finding the derivative of the function.

Q: Evaluate | e'(sin(1) + e*)°dt using an appropriate substitution.

A: Given : ∫etsin1+et9dt

Q: How many periods of the function y = sin x are there between -10T <0<6T ?

A: Given that y=sinxTo find : number of periods in interval  -10π≤x≤6πSolution : period of sinx is 2πin…

Q: If the function = (x)S x' +1 cos( 2 7x - a) if x < -1 is continuous at if x 2 - 1 x = -1 , find the…

A: Given: fx=cos2πx-aifx&lt;-1……1x3+1ifx≥-1……2   To find: Value of a where fx is continuous at x=-1.

Q: bx + c Given tan 3 - In(x2 - 8x + 25) + 1 -dx %3D x2 - 8x + 25

A:

Q: 2. Use reduction formula to evaluate the integral: sin xdx.

A: We have to evaluate integral by using reduction formula.

Q: Find the indefinite integral ∫ sin 8x cos 7x dx

A: ∫sin8x cos7x dx

Q: Evaluate the integral 1—е-4а sin x cos 3xdx

A:

Q: Find the trigonometric integral ∫x tan4 x2 dx

A: Given: I=∫xtan4x2dx for evaluating given integral, we substitute  x2=t…

Q: tan x sec? x dx

A: Given integral: ∫tan2 x sec2 x dx

Q: The amplitude A and period T of f(x)=5sin(4x) are..................... and ....................

A:

Q: Assume sin(t) = -12 where π < t <3. Compute the following: csc (-t) = cos(t + 2) = tan(t) =

A: We have given  Sint = -1/12 , where π&lt;t&lt;3π/2  Compute  1) cosec(-t)  2) cos(t+π/2)  3)…

Q: Q If find x tan cy2 of +2x the Value dx?

A: Given function is                                                  x2y+3y4=xtany+2x differentiating…

Q: calculate SN given by Simpson’s Rule for the value of N indicated.

A: Given, ∫01cos(x2)dx  and N = 6 Solution: Simpson's rule: Area = ∫abf(x)…

Q: Derive a formula for tan x sec" x dxr where n# 0.

A: Please go through the attached solution. I hope that this solution will help you. Thankyou . Best…

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

A:

Q: Find the indefinite integral ∫tan5 (x/2) dx

A: It is given that, ∫tan5x2dx. We have to evaluate it.

Q: tan³ (In x) sec (In x) dx (8)

A:

Q: (b) 는(cosx)=-sinx (d) VI+ tan x 1+* Q1) Show that: (a) (1+x) =1+6x (e) (V): *- () %3D

A:

Q: (a) Evaluate the integral sin* 4x cos3 4x dx

A: a) Evaluate the integral                                 ∫0π8 sin4 4x cos3 4x dx  Let us substitute…

Q: Find all values of 0 in the interval [0°,360°) that have the given function value. tan 0= 3

A: Given, tan theta= sqrt(3)/3= sqrt(3)/(sqrt(3)×sqrt(3)) tan theta= 1/sqrt(3) [0°,360°)

Q: The integral S (A S- (в x dx x² + √√√x²-1- sino do 1 + cos sec²0 do 1+tano " cose de 1-sino sece…

A: Use trigonometric substitution

Q: Find the indefinite integral: | sin(6x) cos(3x) dx

A:

Q: Given the integral sin(3x + 5) dx cos(3x + 5)

A:

Q: Express the following as an algebraic function of x. sin(arctan(2x) + arccos(2x))

A: Question is solved.

Q: Compute L {sin(2t)e"}.

A:

Q: the integral of tan^2 (x) cos^3 (x)dx

A: To evaluate the given trigonometric integral

Q: a (a) L{sin at}=- s2 +a?

A:

Q: Find the intervals on which f(x) = 5 x + 5 cos(r) increases for 0 < a < 2n.

A: f(x) is increasing if f'(x)&gt;0 in the interval   Note that  -1 less than equal to (sinx) less than…

Q: Find the following integral:

A: Use substitutions to integration

Q: Express the following as an algebraic function of x. sin(arctan(2x) – arccos(2x))

A:

Q: Find dy/dx by implicit derivation. If tan-1(x2y) = x + xy2.

A:

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

A:

Q: d Prove, through the limit process, that (cos x) = - sin x. dx

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: