1) (. . ' Evaluate the following indefinite integrals. g) / sec² x.e²-tan z sin r cos® xdx dx

Q: Find the Indefinite integral. (Use C for the constant of integration.) V tan(5x) sec?(5x) dx

A:

Q: Evaluate the indefinite integral using substitution. (Use C' for the constant of integration.) x2 dx…

A: Given:  Let I=∫x2x3-3 dx To Find: To evaluate the given integral.

Q: (5) Find the indefinite integral (a)fVtan x sec'dx aun 2x sec' 2xdx sin x (c)) cos'x 1 cos-de

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) V tan(8x) sec?(8x) dx

A: We will use the substitution, tan(8x) = u³ and proceed as follows :

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) ecos(st) sin(5t) dt

A: Given : ∫ecos5tsin5tdt

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | x³ sin(x*) dx

A: Let’s put u = x4 and then solve the integration:

Q: r" (tan (x)) (In (cos(x))) dx

A: solve this integration by substitution. substitue                    ln(cos(x)) = t on solving

Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx cos x

A: The given integral is ∫sinxcos5xdx. We know that, ∫xndx=xn+1n+1+c           c=Integration constant.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | Vx19 sin(4 + x21/2) dx…

A: Since the exact one wasn't specified we'll answer the first question only. Please resubmit a new…

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

A: ∫sec7x tanx dxu = sec7xdudx = 7 sec7x tanxdx = 17 sec7x tanx du⇒17∫1 du= u7substituting u = sec2x=…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(2x) cos?(x) 45 + coS

A: we know the trigonometric identitycos2x=2cos2x-1cos2x=1+cos2x2I=∫sin2x45+cos2xdxreplace value in the…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos x dx (sin x)24

A: Given ,  the indefinite iintegral  I= ∫cosxsinx24 dx  Let sinx = z  cosx dx = dz  I =∫dzz24 I =…

Q: 3. Find the indefinite integral. (Use C for the constant of integration.) Ssin(3x) cos(3x) dx

A:

Q: Find the general indefinite integral. (Use C for the constant of integration.) x' dx

A:

Q: Use a table of integrals with forms involving In(u) to find the indefinite integral. (Use C for the…

A: To find the indefinite integral, ∫x6ln(x) dx

Q: Find the indefinite integral using the substitution x = 3 sec(0). (Use C for the constant of…

A: To find the integration (x³√(x²-9))dx With substitution x=3sec(theta)

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) 1 sin dx

A: Let I=∫sin1x6x7dx

Q: - e*) sinh x + e* cosh x + ex In the indefinite Integral in(cosh x + ex). A In(cosh x + e*)- sinh x…

A:

Q: Evaluate the definiteIntegral. integral 1/2 to 1 cosx^-2/x^3 dx

A: The given integral is ∫121cosx-2x3dx. Let u=x-2. Then, du=-2x-3. The lower limit will become…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) COS X dx (sin x)20

A: Given, ∫cosxsinx20dx We have to evaluate the indefinite integral.

Q: Find the indefinite integral ∫ sech2x / tanh x dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration. sin(2x) sin(cos(2x)) dx

A: To evluate: I=∫sin(2x) sin(cos(2x)) dx...(1)

Q: Find the indefinite integral. (Use C for the constant of integration.) an(x) In cos(

A: The given integral is: I=∫9tan xlncos x dx

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) (sec(x)tan(x) – 8…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin20(x) dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dx +7 tanx

A: we find out integration of given function.

Q: Find the indefinite integral. (Use C for the constant of integration.)

A: The given integral is,

Q: Find the indefinite integral. (Use C for the constant of integration.) 6 de cos(0) – 1

A: Given integration is : ∫6cosθ-1dθ To find the value of integration. Use trigonometry ratio formula,…

Q: Find the indefinite integral. (Use C for the constant of integration.) (8 cos x + 7 sin x) dx

A:

Q: In the indefinite Integral in(cosh x + e*)- (A sinh x + ex B) In(cosh x + e*) sinh x te* cosh x + ex…

A: D is correct option.

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sec'x tan x dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration. tan(x) cos(x) dx

A: Given,            ∫7tan xlncos x dx

Q: In the indefinite Integral Sin(cosh x + ex)- integrand? A In(cosh x + ex) B sinh x + ex In(cosh x +…

A: The given function whose integral is to be found is called the integrand.

Q: 13. Evaluate the indefinite integral f dx. secx + tanx

A: We have to find the integral

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) dt 9 + tan(t) CoS

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) sin (x) cos(x) dx

A:

Q: Use a table of integrals to find the indefinite integral ∫x arccsc(x2 + 1) dx

A: Consider the given integration as ∫xcsc-1x2+1dx

Q: Determine the following indefinite integrals. Check your work by differentiation. S(se* x - cosx)ctr…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin (5x) J1+ (cos (52))…

A: Here we have to evaluate I=∫sin(5x)1+(cos(5x))2dx

Q: Evaluate the indefinite integral using substitution. (Use C for the constant of integration.) dx - 1

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) | sec2(0) tan²(0) de

A:

Q: Evaluate the indefinite integral using u substitution  x^6sin(x^7) dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x) sin 1 (x) xp

A: ∫cosxsin16x dx

Q: Find the indefinite integral by using appropriate substitutions. (In(sin.x) dx tanx 1) (n(sin(x)))?…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) 5 cosh(/x) xp

A: ∫5cosh(x)xdxlet x=tdifferentiate on both sides12xdx=dtThen ∫5cosh(x)xdx=5∫2cosh(t)dt

Q: Find the indefinite integral. (Use C for the constant of integration.) 15 COS x sin x dx

A:

Q: Find the indefinite integral using the substitution x = 2 tan(0). (Use C for the constant of…

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx 3 + cos x

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.