Download PTU B.Sc (Non-Medical) 2020 March 2nd Sem 76303 Integral Calculus Question Paper

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Roll No. Total No. of Pages : 02

Total No. of Questions : 09

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B.Sc (Non Medical) (2018 Batch) (Sem.-2)

INTEGRAL CALCULUS

Subject Code : BSNM-205-18

M.Code : 76303

Time : 3 Hrs. Max. Marks : 50

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INSTRUCTIONS TO CANDIDATES :

1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students have to attempt any TWO questions.

SECTION-A

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1. Solve the following :
1. Find the length of the arc of the curve y = x² from (0, 0) to (4, 8).
2. Evaluate ?₀¹ ?₀¹ (x+2)dydx.
3. Find the value of ?₀¹ ?₀³ dydx.
4. Evaluate ? x/(x+1) dx.

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5. Evaluate ? sinx dx .
6. Show that ? sin²x dx = 0
7. Evaluate ? x²e^xdx.
8. Prove that ?_a^ß f(y)dx= -?_ß^a f(y)dx.
9. Evaluate ? 1/(a⁴ +x²)² dx.

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10. Write the formula for the volume of the solid generated by the revolution about the x-axis, of the area bounded by the curves y = f(x), y = g (x), and the ordinates x = a, x = b.

SECTION-B

1. Evaluate ?sin^-1vx dx .
2. Find the volume of the spindle shaped solid generated by revolving the asteroid x^2/3+y^2/3 =a^2/3 axis the x-axis.
3. Find the area bounded by the curves y² =4ax and x² = 4ay.

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4. Evaluate ?cosh^-1 [1 +x² ]dx, |x|<1.
5. Evaluate ?₀^p/2 logsinxdx.

SECTION-C

1. If u_n = ?xⁿ sinxdx,n>1. Prove that u_n +n (n—1) u_n-2 =n (p/2) . Hence find the value of u₅.
2. Find the volume of a right circular cylinder with base radius r and height h.

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3. 1. Evaluate ?₀¹ ?_x¹ sin y² dydx by changing the order of integration.
   2. Evaluate ?(x²+ y²)dxdy where R is the region bounded by the four hyperbolas x²-y²=2,9 and xy =2, 4.

NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any page of Answer Sheet will lead to UMC against the Student.

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