2 Evaluate the improper integral e4z dx, if exists. a) The nature of the integral is:

Q: (d) | Ta2 – 4)3 dx -

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

Q: A5. The value of the definite integral dx is b) - 8 c) 24 d) 1.5

A: We have to find the value of the given definite integral.

Q: Evaluate the improper integral: rer dr 8.

A: Explanation of the answer is as follows

Q: 16. Determine the following integrals: (a)Scos 8.xdx. S sin" x.cos.xdx (b)? sec² xdx (c) (d)Se*dx

A:

Q: 2. Find a) ³ dx b) xdx. Hence, find whether the following integrals exist and, if they do, find…

A: To evaluate the given improper integrals

Q: Evaluate the integrals below: (-3) a) dx, b) cosy.eny. dx (xV(1 – (In4x³)² -2 -

A: in part b i integrate with respect to y because it is no sense of integrating with respect to x

Q: B. Given e" (1+ e*)-$dx. Let u = (5). Then, du = Now, we can write ----- ---- the integral as /…

A: Given that       ∫ex(1+ex)-1/3 dx .

Q: 3. Evaluate the improper integral: dx | Tale + 1)'

A:

Q: e (In z)°dæ Evaluate the Integral

A: we have to find the integration of f(x) f(x)=∫0∞ex2(ln x)2dx ∫udv=uv-∫vdu             u=(ln x)2…

Q: For what values of a is each integral improper? Explain.

A: (a) consider the integral ∫a5dxx+2.

Q: 7. Evaluate the improper integral: a. 0 2 (x+2)³ -dx b. 0 5 √√x+5 -dx 3 c. √3 3√/(x-3)* C. $5. dx

A:

Q: dx (§5.7, Q28) Evaluate the indefinite integral: (x – 9)5"

A: step 2 complete solution

Q: b) Evaluate the integrals using substitution: (Hint: rewrite using algebra before determining u) X…

A:

Q: Find the area of the surface that is generated by revolving the portion of the curve y = x2 between…

A:

Q: Which of the following improper integral is divergent? dx A xln(x) 10 dx (B x4 dx D dx

A:

Q: By using u = In x, evaluate the integrals In x dx.

A: ∫x-1xlnx dx Now put, u=lnx⇒dudx=1x⇒du=1x 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.