Evaluate each of the following definite integrals. Must show all of the steps a. 16 dx

Q: dx 1+4x2

A: We have to find out the integral of given function

Q: (x+2)(x+1)²

A:

Q: Solve the following integral: ∫x3(2 - x2)12    dx

A: Given: ∫x3(2-x2)12dx

Q: Stan³ (x)sec?(x) dx 3

A: Topic :- Integrtion

Q: (Inºx– 3lnx) *dx

A: Given that∫ln6x-3lnx4x dxSolution :let…

Q: dx 50. (х — 1)43

A:

Q: Among the given choices, which of the following definite integrals have the smallest value? (A x dr…

A: Given that: (a)∫12xdx(b)∫12x2dx(c)∫12x3dx(d)∫12xdx

Q: Calculate the following integral: (Hints will appear after 3, 6, and 9 attempts.) a sec“(10x) dx

A:

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Write the correct u and du. 3edx -16 2.10-3rdr…

A: We need to solve integrals.

Q: S 42x dx

A: Given,           ∫42x3dx

Q: Evaluate the following integral: ∫ x+8 / x^2+6x+12 dx.

A: ∫ x+8 / x^2+6x+12 dx.

Q: Evaluate the definite integral.

A: Given: I=∫oaxx2+a2dx          , a>0 for evaluating given integral, we substitute x2+a2=t2…

Q: A. Evaluate each of the following definite integrals. 2 1. S (8x3 + 3x²) dx 2. (1+ 2x – 4x²) dx 3. .…

A: Suppose f:a,b→ℝ is a continuously differentiable function, and there exists another function φ such…

Q: 3e"dx ,3x – 16

A:

Q: For each definite integral, find the simplified answer. s dx x2 a) b) c) re In(x) dx d) x²-4x+6 x-1

A: hey since you have posted multiple question I solve 1st 3 subpart.

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Write the correct u and du. 3e3* dx 1. Ve3x –…

A: We will solve the given indefinite integral using the u- substitution.Below find the solution in the…

Q: S(x³ + 2x)*(x² + 4) dx

A: To find integral I=∫x3+2x5x2+4dx

Q: Evaluate the following definite integrals, a. t(1-t)2 dt = V312 dr b. VI- C. 12x-1|dx=

A: Note: As per our guidelines we are supposed to answer only 3 sub-parts. kindly repost the other…

Q: Determine how large the number a has to be so that 1 dx

A: We have to find out the value of a .

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx 2. 4-x-

A:

Q: a) [3 VIn xdx

A:

Q: dx x-1 4

A: Here we take the substitution x-1 = u to solve this integration.

Q: dx 2. x?V4-x2

A: Let x=2sin(u)⇒dxdu=2cos(u)⇒dx=2cos(u) du  and u=sin-1x2 ∫dxx24-x2=∫2cos(u) 2sin(u)24-2sin(u)2du…

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution . 1.

A:

Q: A. Evaluate each of the following definite integrals. 2 S (8x3 + 3x2) dx 1.

A: Given that:

Q: | (3 – t) (2t² + 3) dt 15.

A:

Q: Find the following definite or indefinite integrals: -3 b) S dp (2p+1)2

A: ∫14-32p+12dpLet 2p+1=t⇒2 dp=dt⇒dp=dt2      and at  p=1, t=2×1+1=3at p=4,…

Q: cos(x)dx

A:

Q: Express each of the following integrals as a r function. 8. 9. e- dx Hint: Put x* = u.

A: 8 Given integral is ∫0∞x23e−xdx. The Gamma function is define as follows n=∫0∞xn−1e−xdx Now,…

Q: Find each of the following Indefinite Integrals. (a) 3 - 1 dr rll

A: In the question it is asked to calculate integration of ∫x3-1x11dx.

Q: Sx? sin x dx

A: Use integration by parts

Q: Evaluate each of the following indefinite integrals. S V2 – 3x dx

A:

Q: dx 2x x2

A: Let I=∫1-12xdxx2

Q: Solve the following integral xe* dx 1

A: Calculate the integral         ∫12xex3 dx

Q: Find the definite integral of S: (2x – 1)' dæ 2 112

A:

Q: x3-8 dx x-2

A: ⇒ Expand x3-(2)3 = (x-2)(x2+2x+22). ⇒∫xndx = xn+1n+1 +C   ; Where C is constant of integration.

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. 1. dx 2. x²/4-x?

A:

Q: (x2 + 2x - 2)dx 3

A: The objective is to evaluate the definite integral .

Q: S 3* 2*dx

A: We have to use the exponential rule of integration . From the exponential rule of integration we…

Q: 3 x* +5x dx 1

A:

Q: x*+5x

A:

Q: 4 1 dy 11. 1

A: 11. We need to evaluate the following integral ∫14y5 - 1y3dy

Q: EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Show step by step solution. dx

A:

Q: 10. 0 – 3x6 2.

A:

Q: Evaluate the following definite integral: el0 3 dx Number

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

Q: dx 4+e=* A 4+e-* В D 4e+1 E) None

A: We have to find the integral

Q: x2-4x -dx (x+1)(x²+4)

A: I=∫x2-4xx+1x2+4dxTake the partial fraction of above integral…

Q: d) |r – 2| dx

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

Q: Find each of the following integrals: dx (x² + 9)² a.

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.