60. The study of sawtooth waves in electrical engineering leads to integrals of the form t sin(kot) dt where k is an integer and w is a nonzero constant. Evaluate the integral.

Q: Evaluate the integral. Зп /4 6 sin (x) cos (x) dx Jn/2

A:

Q: (In 1ºx+ 4lnx) *dx

A: Given: - The integral is, ∫(ln10x+4ln(x))8dxx To find: - The solution of the given integral. include…

Q: 3 Which of the following is equal to sec 2 x tan?x dx to obtain the correct indefinite integral? A)…

A:

Q: tan (In 4x) cos (In |(2x)"|)|+C. what is b? The integral of dx is b In A B 2 4 4

A: Given :  ∫tan(ln|4x2|)xdx=bln(|cos(ln|(2x)a|)| +C   To find : Value of b

Q: Evaluate the integral. In 2 2 e sinh 0 d0 - In 10

A:

Q: 7/2 2. Is cot x dx an improper integral? Explain.

A: Given integral is not an improper integral.

Q: Evaluate the integral sin^4 e de from 0 to π/2 * 2π/3 TT/4 31/16 31/5 O h

A:

Q: 1 Determine the definite integral of 4 3(Vx) xp (DE + x^)S

A: Let I=∫49x+13xdxApply the Sum Rule:…

Q: Evaluate the integral. ∫0 π/2 Cos2 θ   dθ

A:

Q: I know it’s u-sub, but I forgot how...

A: Given information:The given integral is

Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: We have to solve the integral

Q: evaluate the integral fromn 0 to pi/2 (cosx)^3

A:

Q: 6. Evaluate the fallowing real integrals by residue theerem ? dX ニ ans : こ。(X+a?)2 493 • I- ans B 12…

A: Let's find.

Q: Evaluate the integral from 0 to pi: ∫cos4(2t)dt

A: ∫0πcos42t dt

Q: 2. Evaluate the integral of 5 sin4x cosx dx if upper limit TO and lower limit = 0. а. 4т/315 b.…

A:

Q: Find the indefinite integral L 교리ln(2x)dz 4 O In(4) O None of the Above

A:

Q: Evaluate the integrals ∫√(1 + cos (t/2)) dt

A:

Q: 2x(x+, こメP

A: Solve

Q: Use integration by parts to evaluate the integral. 6 3 e cos x dk 0

A: Given integral is

Q: 2. Evaluate the integral: (a) ſe -3x sin 5x dx

A: Multiple questions-"As per our guidelines we are suppose to answer only one question.Kindly re-post…

Q: Find the indefinite integral

A:

Q: Ja cos³ 0 sin 20 de

A:

Q: Evaluate the integral of sin^5 xdx from x = pi/3 to x=2pi/3 a. 0.345 b. 0.178 c. 0.846…

A:

Q: (4) / | Va In x da (d) In x dx x2 (e)

A:

Q: 22) By using an appropriate substitution, the definite integr al Sin (3x) Ccos (3x)-1) dx can be…

A:

Q: Consider two integrals: (a) So sin x dx -2пл+1 (b) +1 sin ædæ. Given that n is an integer, which…

A: The objective is to check which integral is greater.

Q: 5. Evaluate the Integral ?(x²-2)"dx

A:

Q: Find the indefinite integral. 5. 3 dt 12 +C

A: Formula: ∫(1/x) dx =lnx ∫xndx = xn+1/n+1

Q: Q4: a)Evaluate the integral: ( In(cosh2x) coth2x dx b) prove that sec-1x = cos-1! = Cos

A:

Q: 6. Evaluate the fallowing real integrals by residue. theerem 3 -bm -am 응) Co3 mX ans : X Sin mx ans…

A:

Q: 39. | sec'x dx

A:

Q: d) Determine the infinite integrals of the following e+2 i. ii. 2 3 sin2x dx

A: Evaluation of the integral

Q: d) Determine the infinite integrals of the following i. ii. JF 3 sin2x dx

A: Evaluate the definite Integral

Q: Evaluate the integrals ∫7 cos7 t dt

A: We have to evaluate the integral: ∫7 cos 7t dt Solving by substitution method, Assuming, z=7t…

Q: Evaluate the integral of sin 6 (x) dx from 0 to Tt/2. * 5п/32 2n/17 T/32 3Tt/32

A: Given: The objective is to integrate the function sin6(x)dx from 0 to π2.

Q: 11. The integral of tan(In|4x²|) dx is bln|sec(ln(2x)ª)|. What is b? А. 2 В. 1 D. ! С.4 4

A:

Q: 7. Find the indefinite integral. (a) / 3 cos(") dz /32c0 31 dr

A:

Q: The resulting integral of sin-cos-sino de 2 2 has the form -(0)+ C· What should be the value of o to…

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: du 2. f 1-cos? 2u

A:

Q: 5. Evaluate the following integrals3 sin ttZ dz C: İz-il 471 =D2 ans: C. 3. coshz -27 ans : Icz²3iz

A: By residue theorem, we can solve these problems.

Q: Evaluate integral S (2 sin a + 4 cos z) dæ

A:

Q: -cos-sino de has the form sin 2 2 -F(0) +C. What should The resulting integral of 4 be the value of…

A:

Q: 2 58 n lim dx !! (n+1)? j=1 and the value of the integral is

A:

Q: a) Evaluate the integrals using appropriate substitutions. Sine ii) S - de Cos20+1

A:

Q: Evaluate the integrals 5./ (를 -5cos x) dx 2 1 1 6. sin? cos? x x

A:

Q: Evaluate the integral (exact value). e6sin (87) + C e6x sin(8x) dx 7

A: We can find the integral as below using integration by parts as below.

Q: (8) 18. Evaluate the following indefinite integrals: (a) / (5e* +7z + 1le") dr dr

A:

Q: Evaluate the definite integral. integral (lower 0, upper 3) t^3 sin(t^4) dt  =

A: We have to solve the definite integral

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.