Chapter Study

BCA Semester 2 – Mathematics II – Unit 4: Integration and Its Applications (8Hrs)

Comprehensive questions and detailed answers for Unit 4: Integration and Its Applications (8Hrs). Perfect for exam preparation and concept clarity.

5

Questions

30

Marks

Back to All Chapters

1

Evaluate:

\quad \text{a) } \int_0^2 \frac{dx}{x^2-25}

\quad \text{b) } \int \frac{2x+5}{x^2+5x} \, dx

MediumNumerical5 marks2022(TU FOHSS Final)

2

Evaluate the integrals:

\text{a) } \int \frac{2x+5}{\sqrt{x^2+5x}}\,dx

\text{b) } \int e^{2x}\log x \, dx

MediumNumerical5 marks2023(TU FOHSS Final)

3

Evaluate the following integrals:

\quad \text{a) } \int \frac{2x+3}{x^2+3x}\,dx

\quad \text{b) } \int e^x \cos x \, dx

MediumNumerical5 marks2024(TU FOHSS Final)

4

a) Find the area of the region between the curve

y = 4 - x^2,\quad 0 \le x \le 3

and the $x$ -axis.
b) Solve:

\frac{dy}{dx} = \frac{x^2 + y^2}{2x^2}

HardNumerical10 marks2024(TU FOHSS Final)

5

Find the area of the region enclosed by the parabola $y = 2x^2$ and the line $y = x$ .
Evaluate:

\text{a)} \quad \int_{0}^{2} \frac{dx}{\sqrt{x^2 + 4^2}}

\text{b)} \quad \int x^2 e^x \, dx

MediumTHEORY5 marks2024(TU FOHSS Final)

Showing 5 questions

Sample Questions

Evaluate: \[ \quad \text{a) } \int0^2 \frac{dx}{x^2-25} \] \[ \quad \text{b) } \int \frac{2x+5}{x^2+5x} \, dx \]

Marks: 5Chapter: Unit 4: Integration and Its Applications (8Hrs)

Evaluate the integrals: \[ \text{a) } \int \frac{2x+5}{\sqrt{x^2+5x}}\,dx \] \[ \text{b) } \int e^{2x}\log x \, dx \]

Marks: 5Chapter: Unit 4: Integration and Its Applications (8Hrs)

Evaluate the following integrals: \[ \quad \text{a) } \int \frac{2x+3}{x^2+3x}\,dx \] \[ \quad \text{b) } \int e^x \cos x \, dx \]

Marks: 5Chapter: Unit 4: Integration and Its Applications (8Hrs)

a) Find the area of the region between the curve \[ y = 4 - x^2,\quad 0 \le x \le 3 \] and the \(x\)-axis. b) Solve: \[ \frac{dy}{dx} = \frac{x^2 + y^2}{2x^2} \]

Marks: 10Chapter: Unit 4: Integration and Its Applications (8Hrs)

Find the area of the region enclosed by the parabola $y = 2x^2$ and the line $y = x$. Evaluate: \[ \text{a)} \quad \int{0}^{2} \frac{dx}{\sqrt{x^2 + 4^2}} \] \[ \text{b)} \quad \int x^2 e^x \, dx \]

Marks: 5Chapter: Unit 4: Integration and Its Applications (8Hrs)