Sain sin 7x dx 1 1 (e) dx cos? x sin?

Q: (d) | Ta2 – 4)3 dx -

A: To Determine: Convert the indefinite integral into definite integral using the interval [0,1]…

Q: Use a table of integrals to find the indefinite integral.

A: Integration is summation of discrete data. The integral is calculated for the functions to find…

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos' (0) sin(0) dO

A:

Q: Find the indefinite integral using the substitution x = 4 sin θ.

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(In 12x) dx Cos In x +…

A:

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

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Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(t) sqrt{1+cos(t)} dt

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

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin(2x) dx 27 + cos (x)

A:

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

A: ∫tan8xcos9xdx

Q: Evaluate the definite integral.

A:

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

A: ∫tan8xcos9xdx

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

A:

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: Find the indefinite integral using the substitution x = 4 sin θ.

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) | (2 cos x + 9 sin x) dx

A:

Q: Find the indefinite integral. (Use C for the constant of integration.) (4 cos x + 3 sin x) dx

A:

Q: Evaluate the indefinite integral.

A:

Q: Evaluate the integral. (Use C for the constant of integration.) 9 cos X dx 3 + sin x

A:

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: (c) / cos(3t) + sin(5t) dt (f) (tanr+cot r) dr

A:

Q: Evaluate the integral. (Use C for the constant of integration.) | tan (x) cos°(x) dx

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) tan-(5x) dx 1 + 25x2 1 2…

A:

Q: Find the indefinite integral using the substitution x = 6 sec(o). (Use C for the constar…

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) (4). 1 sin dx

A: Indefinite integral

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos (0) sin(0) de

A: Given query is to find integral of the expression.

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: (c) dx 1 – x2 (d) | Va? + x² 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 integrals using Substitution. (use C for the constant of integration.) a) |…

A:

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

A:

Q: Use the table of integrals to evaluate the integral. (Use C for the constant of integration.) [ 7…

A:

Q: Evaluate the integral.  integral  (1- sinx )/ cos x  dx

A: ∫1-sinxcosx dx

Q: sin(8x) + cos(7x) dx COS Зх — 5 sin dx 2

A:

Q: (e) / V1 + x² dx (f) x² + 4 dx

A:

Q: Evaluate the integral. integral 0  to pie /2    cos x + sin x dx

A:

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

A:

Q: (a) /(3=² (За? — 6х + 5) dx - 1 .5 x° + 5 1 (b) dx - 4

A: To determine the value of definite integrals.

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

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) cos(x)/sin^20(x)    dx

A:

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

A:

Q: Evaluate the indefinite integral. (Use C for the constant of integration.) sin (9.r) J 1+ (cos…

A:

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

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Q: Evaluate the definite integral. integral 0 to 1  ( x divided by 1+2x2) 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: Evaluate the integral - dx · 1- sin x cos X

A: The given integral,       ∫cos x1-sinxdx

Q: Find the indefinite integral. (Use C for the constant of integration.) (5 cos x + 7 sin x) dx

A: ∫5cosx+7sinx dx∫5cosx dx+∫7sinx dx

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.