ISC Class 12th Mathematics Chapter 7 - Applications of Integrals Important Questions with Answers

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Evaluate:

`int_0^1x^2dx`

Question 2.

Hence find the area bounded by the curve, y = x |x| and the coordinates x = ?1 and x = 1.

Question 3.

Using the method of integration, find the area of the triangular region whose vertices are (2, -2), (4, 3) and (1, 2).

Question 4.

Draw a rough sketch of the curve and find the area of the region bounded by curve y² = 8x and the line x =2.

Question 5.

Sketch the graph of y = |x + 4|. Using integration, find the area of the region bounded by the curve y = |x + 4| and x = –6 and x = 0.

Question 6.

Find the equation of an ellipse whose latus rectum is 8 and eccentricity is `1/3`

Question 7.

Show that the rectangle of the maximum perimeter which can be inscribed in the circle of radius 10 cm is a square of side `10sqrt2` cm.

Question 8.

Draw a rough sketch of the curve y² = 4x and find the area of region enclosed by the curve and the line y = x.

Question 9.

Express `(2+"i")/((1+"i")(1-2"i")` in the form of a + ib. Find its modulus and argument

Question 10.

Express the complex number `(1+sqrt3i)^2/(sqrt3 -i` in the form of a + ib. Hence, find the modulus and argument of the complex number.

Question 1.

Find the equation of the standard ellipse, taking its axes as the coordinate axes, whose minor axis is equal to the distance between the foci and whose length of the latus rectum is 10. Also, find its eccentricity.

Question 2.

P, Q, and R represent switches in on position and P’, Q’ and R’ represent switches in off position. Construct a switching circuit representing the polynomial PR + Q (Q’ + R) (P + QR). Using Boolean Algebra, simplify the polynomial expression and construct the simplified circuit.