tan x sec" 2x S sec*x dx- sec" x dx п — 1 (n + 1)

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: To evaluate the integral∫0∞x3(x2+1)2dx

Q: fx sin(5x)dx

A: use integration by parts take

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. 00 3x dx = (x² +…

A:

Q: Evaluate the integral. ∫0 π/3 tan5 x Sec4 x dx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 6 tan(x) sec³(x) dx

A: We have to find

Q: Use integration by parts to show that for n > 2: / sin" x dx: 1 sin- x cos x + /sin-2 x dx.

A: To evaluate: ∫sinnx dx

Q: ) Use integration by parts to verify the reduction cosxsin x n-1 Scos" xdx=!

A: Here I=∫cosndx ⇒I=∫cosn-1x×cosx dx using integration by part;

Q: Use integration by parts to show that, for n > 2, 1 cos a sin"-1 n 1 sin"-2 xdx. n - sin" xdx = x +…

A:

Q: Determine whether the integral is convergent or divergent. x arctan(x) 63 dx (1 + x2)2

A:

Q: Use the tabular method to find the indefinite integral. ∫x3 cos 2x dx

A:

Q: Evaluate the integral 6. dx x2 V16x2 – 9 | Note: Use an upper-case "C" for the constant of…

A: Solve the given integral

Q: Use integration by parts to establish the reduction formula: Jx" cos x dx = x" sin x – n x"-1 sin x…

A:

Q: Find the integral m tanx X, 1+x?

A: Given :

Q: Use integration by parts to prove the reductionformula.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: Use the Trapezoidal Rule to evaluate the integral [x-'dx. .-1 1

A: Equation is f(x)=1xThe value of the table for x and y x 1 1.25 1.5 1.75 2 y 1 0.8 0.6667 0.5714…

Q: •4 x dx 10 x2 – 9

A:

Q: Find the integral of * dx 2 sin x – cos x - |tan + 2 + v5 + C tan + 2- V5 In | tan + 2+ v5 |tan + 2…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | 2 tan (x) sec®(x) dx C must be in…

A:

Q: Use Trapezoidal Rule with (n- 4) to find the integral dx x-1

A:

Q: Use integration by parts, together with the techniques of this section, to evaluate the integral.…

A: Given: Let, By the rule of integration by parts.

Q: Determine whether dx is convergent or divergent. If it is convergent evaluate the integral Vx 3. 4…

A:

Q: sec?x dx 1- tan x b. Determine whether the integral converges or diverges.

A:

Q: Evaluate the integral –4x3/2 In(x) dx, x >0 Note: Use an upper-case "C" for the constant of…

A: Evaluate the integral

Q: Use integration by parts to evaluate the integral. (7) [x sec x tan x dx

A:

Q: Determine whether integral 0 to pie /2 sec x dx    converges or diverges

A:

Q: use the Comparison Test to determine whether or not the integral converges.

A:

Q: Evaluate the integral ( Use C for the constant integration) ∫ 11 tan4(x) sec6(x) dx

A: I=∫11tan4x×sec6x dx=11∫tan4x×sec4x×sec2x dx=11∫tan4x×1+tan2x2×sec2x dx                      ⋯⋯(1)

Q: 1 dx 7x° +9x x² +3 dx 2 2x* +x

A: Explanation of the answer is as follows

Q: Explain why the improper integral (x + 3) sin(x) dx L. (x² + 1)(x² + 4)² is convergent. 8

A:

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Here given integration as I=∫2∞1xx2-4 Since ∫1xx2-a2=1asec-1xa+C

Q: | de P8- メレー Oe dedx

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 2 tan3(x) sec(x) dx

A: Let sec(x)=t sec(x)tan(x)dx=dt tan2(x)=sec2(x)-1 Substituting we get 2 int (t2-1)dt =2 (t3-t)+C…

Q: Evaluate the integral. (Use C for the constant of integration.) dx 3 - 3x9

A:

Q: Evalate the integral (tanx dx by using the reduction formıla of tangent fumction. х

A: Let u=tan(x). then x=tan-1u and  dx=tan-1u'du=duu2+1

Q: Determine whether it converges or diverges. You must provide justification for your answer. sin(x)…

A:

Q: Use integration by parts to prove the reductionformula.

A:

Q: Use the definition of the definite integral to evaluate ∫02 (3x2 +1)dx. Use a right-endpoint…

A: As a first step, let's plot the graph of the curve given to us. Let's call the curve y = f(x) = (3x2…

Q: Perform the integration. TT 3 sec³x tan x dx 2 + sec x 0

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 8 tan(x) sec³(x) dx

A:

Q: 2. Use the composite trapezoidal rule to estimate the integral of y = sin(x) %3| from x = 0 to 2.…

A:

Q: cises 1–12 con- of the Integral

A:

Q: Use the Comparison Theorem to determine whether the integral is convergent or divergent. arctan(x)…

A:

Q: Evaluate the integral that converge dx (2x- 1)3

A:

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A:

Q: Evaluate the integrals that converge, enter 'DNC' if integral Does Not Converge. -x2 2xe dx

A: Given integral  ∫0∞2xe-x2dx We have to find integral for converges or diverges.

Q: Use integration by parts, together with the techniques F, G Qof this section, to evaluate the…

A: Use integration by parts, together with the techniques F, G Qof this section, to evaluate the…

Q: Determine whether the improper integral diverges or converges. Evaluate the integral if it…

A: Integration:       ∫3∞ 1xx2-9dxLet us keep the substitution,…

Q: Use integration by parts to evaluate the definite integral: ∫3se^-4s ds with an upper limit of -0.9…

A: A=3∫abse-4sds , solving A where a,b are upper and lower limits as per questionIntegrate by parts…

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.