# Category Archives: School Learning

Question 11. Sketch the region {(x, y) : 9x2 + 4y2 = 36} and find the area enclosed by it, using integration. Solution: 9×2 +… Read More
Question 1. Using integration, find the area of region bounded between the line x = 2 and parabola y2 = 8x Solution: Here, Given equations… Read More
Prove the following by the principle of mathematical induction: Question 1. 1 + 2 + 3 + … + n = n (n +1)/2 i.e.,… Read More
Question 21. If  and  , find  Solution: Here, Differentiate it with respect to t using chain rule, And, Differentiate it with respect to t using quotient rule,… Read More
Question 21. Draw a rough sketch of the curve  and find the area between x-axis, the curve and the ordinates x = 0, x = π… Read More
One comes across various forms of sound in its daily lives, and everyone is well-equipped with a system to recognize various types of differences in… Read More
Question 1. Find , when: x = at2 and y = 2at Solution: Given that x = at2, y = 2at So, Therefore, Question 2. Find ,… Read More
Question 1. Show that  and  are coplanar. Also, find the equation of the plane containing them. Solution: We know, the lines  and  are coplanar if: Since, , the lines are… Read More
Question 1. Evaluate the following determinant: (i)  Solution: Considering the determinant, we have As R1 and R2 are identical Hence, △ = 0 (ii)  Solution:… Read More
Question 11. Find, when and Solution: Here, Differentiating it with respect to t using quotient rule, and, Differentiating it with respect to t using quotient rule,… Read More
Derivative of a function f(x) tells us how will the value of the function change when we change x. This quantity gives us an idea… Read More
Graphs are an integral part of calculus. They help us in analyzing the functions behavior and limits and lots of other things. We know graphs… Read More
Question 1. Differentiate f(x) = x4 – 2sinx + 3cosx with respect to x. Solution: Given that, f(x) = x4 – 2sinx + 3cosx Now,… Read More
Evaluate the following integrals: Question 41. ∫cos-1⁡((1 – x2)/(1 + x2))dx  Solution: Given that, I = ∫cos-1⁡((1 – x2)/(1 + x2))dx) Let us considered x… Read More
Question 1. Show that f(x) = |x – 3| is continuous but not differentiable at x = 3. Solution: f(3) = 3 – 3 =… Read More