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Calculus II Test 1: Partial Fractions, Integration and Area Calculation, Exams of Calculus

Acharya Nagarjuna UniversityCalculus

A calculus ii test focusing on partial fractions, integration, and area calculation. Students are required to simplify expressions, evaluate definite integrals, and find the area of a region bounded by two intersecting parabolas. No calculators, books, or notes are allowed. Justify answers with appropriate arguments and steps.

Typology: Exams

2012/2013

Uploaded on 03/20/2013

shreya
shreya 🇮🇳

4.2

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Calculus II Test 1 NAME_________________________________
No calculators, books, or notes allowed. Justify your answers by giving
appropriate arguments and steps. Circle answers
PART I: Short problems. Simplify and circle answers. No partial credit.
Four points each.
1. Put in correct partial fraction format, but do not solve for the unknown
constants 1
x(x+3)(x+9) :
2. Evaluate R2
1x3dx:
3. Let g(x) = Rx3
1
1
ps2+1 ds and …nd the derivative g0(x):
1
pf3
pf4
pf5

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Calculus II Test 1 NAME_________________________________ No calculators, books, or notes allowed. Justify your answers by giving appropriate arguments and steps. Circle answers PART I: Short problems. Simplify and circle answers. No partial credit. Four points each.

  1. Put in correct partial fraction format, but do not solve for the unknown constants (^) x(x+3)(^1 x+9) :
  2. Evaluate

R 2

1 x

(^3) dx:

  1. Let g(x) =

R (^) x^3 1 p^1 s^2 +1 ds^ and Önd the derivative^ g

(^0) (x):

  1. Find

R

sin^3 x dx

  1. Find

R

cos(5x + 2) dx

  1. Put in partial fraction form. Do not solve for the unknown constants 1 x^2 (x+1)^2 (x^2 +2) :
  2. Evaluate

R 5

2

1 x dx

PART II. Partial credit possible. Simplify and circle your answers. Ten points each.

  1. Find

R

x^3 (1 x^4 )^7 dx:

  1. Find

R

x cos(3x) dx:

  1. Find

R 1

x^2 (x+3) dx:

  1. Let A > 0 be a positive number. The curves y = A^2 x^2 and y = x^2 A^2 intersect to form the boundary of a Önite region. Sketch the graph and Önd the area of the region.