Class XII Mathematics

Chapter 6: Integrals

Standard NCERT & CBSE aligned study curriculum. Master concepts, track accuracy, revise weak areas, and challenge yourself with 9 customized practice modes.

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Worksheet Details:

  • Title: Class XII Math: Integrals Printable Sheet
  • Format: Print Optimized CSS stylesheet
  • Sections: Formulas checklist, 5 assessment questions, worked keys

NexPro Education Worksheet

Class XII Mathematics: Integrals

Name: ______________________Date: __________________Score: ______ / 5

Section I: Key Formulas

Integration by Parts
\int u v \, dx = u \int v \, dx - \int (u' \int v \, dx) \, dx
Definite Integral Fundamental Theorem
\int_{a}^{b} f(x) \, dx = F(b) - F(a)

Section II: Answer the Questions

1. Using integration, find the area of region bounded by line y = 3x , the curve y = 24 x- and y- axis in first quadrant.

Solve and write the step-by-step solution in the workspace below.

2. Make a rough sketch of the region {(x,y ):0 ≤y≤x2+ 1,0 ≤y≤x+1,0 ≤x≤ 2} and find the area of the region using integration.

Solve and write the step-by-step solution in the workspace below.

3. Using integration, find the area of the region bounded by the curve 24y x= - , the lines x = - √2 and x = √3 and the x-axis.

Solve and write the step-by-step solution in the workspace below.

4. Using integration, find the smaller area enclosed by the circle x2 + y2 = 4 and the line x + y = 2.

Solve and write the step-by-step solution in the workspace below.

5. Evaluate the following integral: /3 /6 1 1 tan dx x π π +∫

Solve and write the step-by-step solution in the workspace below.