Evaluate the integral, where E is enclosed by the paraboloid z = 7+ x2 + y?, the cylinder x? + y? = 5, and the xy-plane. Use cylindrical coordinates. e dv Step 1 In cylindrical coordinates, the paraboloid z = 7 + x? + y? has the equation z = 9+ y2 7+ 2 and the cylinder x + y = 5 has the equation r=V5 Step 2 Therefore, the region E enclosed by the paraboloid, the cylinder, and the xy-plane is described by E = {r, 0, 2)| 0 s zs 7+r OsrsV5 Osos 27 7+ 2 Step 3 To evaluate e dv= er dz dr de, we first calculate the innermost integral. er dz =

Q: Option 2: Problem Solving You wish to invest P10,000 for a period of 5 years. Which of the following…

A: The principal amount we have is ₱10000 and the time period is 5 years.  Therefore,  P=₱10000 t=5

Q: g+y= 쓸 - zxe - 5

A:

Q: Determine, with justification, whether the series converges absolutely, converges conditionally, or…

A:

Q: Evaluate the integral ∫dx/1+2x2.

A: Given :

Q: ∫sinxcosxdx evaluate the integral

A:

Q: Evaluate the integral: 3xe-/4 dr

A: we will do it by integration by parts ∫uv=u∫v-∫u'∫v

Q: determine the integration c Sinx

A:

Q: X-1 2X14 の

A:

Q: 23. į un's da

A: To evaluate the given integral.

Q: 1 (x²+y*) dx dly -1 2

A: Consider ∫-11∫24(x2+y2) dx dy = ∫-11x33+xy224 dy = ∫-11643+4y2-83-2y2dy = ∫-11563+2y2dy =…

Q: dr Vr - 9

A: Given: I=∫drr3-9   ...1   As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: dydr

A: Given, I=∫12∫x221y2·exydydx

Q: би + 12 du

A:

Q: Evaluate the integral ∫cosh2xdx.

A:

Q: Evaluate the impreper integral de 8.

A: It is given that, ∫-∞∞xx4+1dx Let's make a substitution at x. Let us consider, x=tan θ  ...(1) This…

Q: Define and explain integral and its properties briefly

A: Explanation of the answer is as follows