Find the integral for the following functions: - sin(x). esec(x) 1). 1) S cos (x)

Q: Use an appropriate substitution to show that the value of the following definite integral has value…

A: SOLUTION-

Q: Find the following indefinite integrals. (i) (ii) | cos (2x) sin (2xr) dx

A: According to question  given :(i) ∫xex21+ex2dx(ii) ∫cos3(2x) sin2(2x) dx

Q: Find the following definite integrals using an appropriate substitution. (a) /2 cos a sin(sin x) dx.…

A: a) The given integral is ∫0π2cos(x)sin(sinx)dx. Evaluate the integral as follows. Apply u…

Q: Find the integral using the substitution u = t8. Enclose arguments of functions in parentheses. For…

A: According to question,Given integral,∫t7 cost8 dt

Q: 2, .cos' xdx 12. 2

A: Given: Let I=∫-π2π2 cos3x dx To Find: To evaluate the given trigonometric integral.

Q: f sin x ln(cos x) dx

A:

Q: Evaluate the following integrals sin³ (x) cos³(x) dx

A: Given ∫sin3xcos3xdx

Q: 1 sin Tx cos TIx dx 0,

A:

Q: I. Evaluate the following integrals. Check by differentiation. S sin 50 cos 50d0

A: Given;            ∫sin 5θ cos 5θ dθ Apply u-substitution: u=cos 5θ⇒du=-5 sin 5θ dθ            =∫-u5…

Q: Find the integration of the following   x2 / x sin x + cos x

A: Our Aim is to integrate the following expression given below:-x2x sin x+cos x -(i)

Q: Which of the following integrals are improper? Why?  integral 0 to 1  tan x dx

A:

Q: In evaluating the indefinite integral / sin x cos x d , the appropriate u – substitution and. the…

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Q: :Find the integral for the following functions: - Se3x .sinh(x) dx

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Q: Find the following indefinite integrals.

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Q: Find the following indefinite integral. +2e -0.1x dx

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Q: S cos(3=)dz

A:

Q: find formulas for the functions represented by the integrals.

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Q: Evaluate the following trigonometric integrals L cos³(x}sin³(x)dx a) ( sin (x) b) -dp- Av cos?(x)

A:

Q: Find the value of the positive integer A so that: In A 1 sinh x dx 4 Jo

A: ∫0lnA sinhx=14 coshx0lnA=14 coshlnA-coshln1=14 coshlnA-cosh0=14 coshlnA-1=14 coshlnA=14+1…

Q: Evaluate the given integral. ∫ (x cos x + x sin x) dx.

A:

Q: In the following equation/s, find the indefinite integral :-   see the equation attached here

A: We have to calculate the given integral   the given integral is

Q: Evaluate the indefinite integral 5e^5x*sin(e^5x) *dx

A:

Q: Q1: Evaluate the following integrals by using a substitution to reduce it to sec X dx 1 standard…

A: We have to use substitution method.

Q: ii) sin5x cos*x dx

A:

Q: evaluate the integral.

A: To evaluate the given integral.

Q: Evaluate the integral e^2x sin(4x)dx from 0 to pi.

A: Use integration byparts again and again you will get again an integration in the form of I ...as I…

Q: Evaluate the following integral sin x cos x dx

A: The given integral is It can be written as

Q: The integral of the function cos² x. sin a dx is

A: the given expression is: ∫cos2x.sinxdx

Q: |/ (cos(x) + sin(x))² dx

A: *Used the (a+b)2= a2 + 2ab + b2 formula.

Q: Evaluate the following indefinite integral. Sx*tan"x dx

A: given problem is solved with the help of integration by parts    i.e. ∫udv = u.v-∫v.du where u =…

Q: sin x+cosx dx sin x-cosx vi.

A:

Q: Evaluate the following improper integral. If it diverges, then type 'DNE. Otherwise, find its exact…

A: Gven that∫0189dx1+x2tan-1xSolution:∫0189dx1+x2tan-1xlet,…

Q: Evaluate the definite integral on the interval [0, pi/4] sin(t) / cos^2(t)  dt

A: By substitution, we calculate the value of given integral.

Q: Evaluate the following indefinite integral. -x-2 (a) dx dx (b) cos 0 sin Od0

A:

Q: Evaluate the integral: a cos (4) dx x² sin² ( ÷) where a is a nonzero constant.

A: Given,  ∫  a cosaxx2 sin2axdx

Q: e" cos(e“)dx

A: Let I=∫0∞excosexdx  Put   ex=t⇒exdx=dt When x=0, t=e0=1 When x=∞, t=e∞=∞ So, by substitution, the…

Q: sin*(x) cos²(x)dx 4 CO

A: To evaluate the integral ∫ sin4(x) cos2(x) dx

Q: Q3: Find the integral for the following functions: - 1 3)S sinh(x)-cosh(x) ax

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Q: Evaluate the following integral by using Odd and Even Powers Method: y = [ cos³ (;x) dx

A:

Q: 3) Evaluate the following integrals. a) | cos(tan(x)) sec (x) dx

A: Given that ∫cos(tanx) sec2x dx first let us simplify and then integrate

Q: 20. Evaluate the following definite integral: , sec?x dx

A:

Q: For ſ sin" (0) cos (0)d0, use a suitable change of variables to determine the indefinite integral.

A: Given : ∫sin7θcosθdθ

Q: cos“(x) sin(x)dx

A: See attached file for a step by step explanation to find the given integral.

Q: Evaluate the following indefinite integral | 8 sin(x) – 2 cos(x) dx =

A: We have to find integral