V16 – x² dx

Q: Simplify the following expression d/dx of the integral from 0 to x2 sin(t3)dt

A:

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: 1 sin Tx cos TIx dx 0,

A:

Q: xªe¬ª dx x=0

A:

Q: Approximate the following integrals using the Trapezoidal rule. r0.35 2 dx x2-4 1. 2. Sfx sin(x) dx…

A:

Q: Evaluate the given integral. Use exact values. – 2x – 14 dx (x + 3)(x – 5) +C

A: topic - indefinite integral

Q: sin(6x) Vi? +4 dt 7

A:

Q: sin x dx e lme

A:

Q: Consider the following integrals 00 4 sin? x i. dx x² + 6 e9t dt ii. e9t – 1 Mark the correct one…

A: Given: i.∫1∞4 sin2xx2+6dx ii.∫01e9t dte9t-1

Q: Find the following indefinite integrals.

A:

Q: Q3) Evaluate the following integral by using Trigonometric substitutions Method. 1 dx Vx2 – 9 y

A:

Q: evaluate the definite integral using the values below. 23 dx = 320, a de = 16, dx = 4 2 34. z da

A:

Q: 12 Which expression represents the trapezoidal approximation T3 to the integral sin (V7) dx?

A:

Q: Evaluate the following integrals sin? x cost x dx

A: Hey, since there are two questions posted, we will answer the first question. If you want any…

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: sin (x) cos/2 (x)dæ sin (x)dx

A: To find the integration

Q: Evaluate the following integrals.

A: Given: I=∫012sin-1x1-x2dx                                              ...1 for evaluating given…

Q: Evaluate the definite integral.

A:

Q: 17 e- dx x=0

A:

Q: Find the integral for the following functions: - ſ e3x . sinh(x) dx

A:

Q: 2 sin? t sec“ t dt

A: To determine:

Q: s) Calculate the indefinite integral using Trigonometric Substitution. X [ dx +x²

A: This is a problem related to integral. Based on the trigonometric substitution we will answer the…

Q: use the Change of Variables Formula to evaluate the definite integral.

A:

Q: Find the following definite integral where A is a constant and A > 2: | (10z + 17z +1) dx = %3D

A: We have to find the integral of∫2A(10x3+17x+1)dx, where A>2. Applying the sum rule of…

Q: Use the substitution a = 4 sec t to evaluate the integral IVI2-16 Note: Use C for an arbitrary…

A: The given integral is: ∫dxxx2-16 Substitute x=4sec t in it.  So, dx=4sec t tan t dt

Q: Find the following indefinite integral. I dx x2 + 9

A: From the given problem:   I=∫xdxx2+9...(1)   Let,   x2+9=t   To differentiate with respect to x.…

Q: 4 3 dx | cos(x) .5 1

A: Let I=∫14cos x-3x5dx

Q: Evaluate the following integrals.

A: ∫esin-1x dx=∫esin-1x·1 dx=esin-1x·∫1 dx-∫desin-1xdx·∫1 dxdx   ∵∫u·v dx=u·∫v dx-∫dudx·∫v…

Q: |/ (cos(x) + sin(x))² dx

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

Q: By using a trigonometric substitution x = 3sece ,where 0 s0 < 27 "he integral 3 Vx² - 9 dx can be…

A: We have to choose the correct answer from the given option according to the given condition

Q: Evaluate the following integrals.

A:

Q: Given 4 cos(x²) dx 2 How many Trapezoids will you need to estimate the definite integral to an…

A: Given the integral I=∫24cosx2dx. (a) We need an accuracy of 0.001 when the Trapezoidal rule. The…

Q: Find the exact value of the definite integral below, using the substitution u = x x (√6+√2) 1+x² -…

A:

Q: Use the substitution x = 3 sin t to evaluate the integral f v9 – x² dx. - Note: Use C for an…

A:

Q: Find the indefinite integral.∫(cos5 t/√sin t)  dt

A: Given information: The indefinite integral is ∫cos5tsintdt Trigonometric identities used:…

Q: Find the integral using trigonometric substitution.

A:

Q: Evaluate the following definite integrals.

A: I =  ∫01xsinπx.dx  ................(1)we know ∫abf(x).dx = ∫abf(a+b-x).dx

Q: Evaluate the following integrals. When using substitutions, be show to show them explicitly. a) + 5…

A:

Q: Evaluate the following integrals using the tabular method. (i) 2x sin 2x dx

A: We need to evaluate the integral ∫e2xsin(2x)dx by tabular method

Q: Væ +1 dx

A: Substitute u=x+1,du=dx2x+1. Here if u=x+1⇒x=u2-1.

Q: Find and simplify the following integrals: S dx 11) (x-2)² 12) ſ cos(2x)e sin (2x) dx

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 3. Evaluate the following definite integrals using a change of variables. а. sin(2x) dx b. xVx+1 dx…

A:

Q: Evaluate the definite integral. t10 sin (t11) dt

A:

Q: Evaluate the following integrals.

A: Given: The integral is:                                                                 I=∫sin x…

Q: Evaluate the definite integral. "Tt/2 " d(sin x)? dx = (sin x)2 dx =

A:

Q: Determine the following indefinite integral. dx |( + x7) dx= O

A:

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

A: Given : ∫sin7θcosθdθ

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.