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Punjab (PTB) · Chapter test · Free

2nd Year Mathematics Chapter 3 TestUNIT 3: INTEGRATION

22 marks · 40 minutes · 18 questions. Covers: UNIT 3: INTEGRATION.

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2nd Year Mathematics Chapter 3 Test

2nd Year · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 22Time: 40 minutes

Q1. Multiple choice questions (Attempt all · 10 × 1 = 10)

  1. The value of a definite integral is always a:

    1. Family of functions

    2. Real number

    3. Variable quantity

    4. Imaginary number

  2. What is the primary objective of using a trigonometric substitution in integration?

    1. To increase the degree of the polynomial

    2. To convert a definite integral into an indefinite one

    3. To eliminate the radical sign in the integrand

    4. To find the derivative of the function

  3. The rule that corresponds to the Product Rule for differentiation is called:

    1. Substitution method

    2. Integration by parts

    3. Partial fractions

    4. Chain rule

  4.  What is the process of recovering a function F from its derivative f called?

    1. Differentiation

    2. Linearization

    3. Antidifferentiation

    4. Integration by parts

  5. The line about which a plane region is revolved to generate a solid is called the:

    1. Axis of revolution

    2. Normal line

    3. Tangent line

    4. Boundary line

  6. The net signed area will be zero when:

    1. The curve does not touch the x-axis

    2. The positive area above the axis exactly equals the negative area below it

    3. The limits of integration are zero

    4. The curve is a straight line

  7. Which pair of identities is used to simplify the expressions after substitution?

    1. Sum and difference identities

    2. Double angle identities

    3. Pythagorean identities

    4. Product-to-sum identities

  8. The mnemonic LIATE is used as a guideline to choose the:

    1. Value of the constant c

    2. First function for integration by parts

    3. Derivative of the function

    4. Limits of integration

  9. According to the LIATE rule, which type of function comes first between Algebraic (A) and Trigonometric (T) functions?

    1. Both at the same time

    2. Trigonometric functions

    3. Algebraic functions

    4. None of the above

  10. What can be calculated using integration to find the space occupied by solids of revolution?

    1. Critical boundaries

    2. Linear approximations

    3. Derivatives

    4. Volumes

Q2. Short questions (Attempt any 6 of 8 · 6 × 2 = 12)

  1. Evaluate the following integrals: 

  2. A patient receives an IV bolus dose of a drug. The concentration in the blood is modeled by  where t is the time in hours since that does was taken. the minimum effective concentraction (MEC) is 3 mg/L. The drug is considered effective if total AUC in a 24-hour period is at least 150 mg-h/L. Find the time T (in hours) when the concentration reaches the MEC.

  3. Evaluate the following: 

  4. A patient is given an intravenous dose oof an antibiotic. The concentration in the bloodstream over time is modeled by:  where t is an hours. Find the total drug exposure (AUC) from t=0 to t=6 hours.

  5. Evaluate the following integrals: Evaluate: 

  6. Evaluate 

  7. Write down the product rule of differentiation and show how it is used to start the derivation of integration by parts.

  8. Sketch the region bounded by the given curves and find the area of the region: