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Integration of inverse trigonometric functions

Integration of inverse trigonometric functions can be calculated using integration by parts ,integration by substitution .Here are the formula for it \[ \int \sin^{-1}x \, dx = x \sin^{-1}x + \sqrt{1 – x^2} + C \] \[ \int \cos^{-1}x \, dx = x \cos^{-1}x – \sqrt{1 – x^2} + C \] \[ \int \tan^{-1}x \,


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Activity 13.6 Class 10 Science

Activity 13.6 from Chapter 13 of the NCERT Class 10 Science textbook focuses on understanding biodegradable and non-biodegradable substances. This activity encourages students to research and explore the environmental impact of different materials, particularly plastics. Activity Description Materials Needed Procedure Observations Students should note down the following information: Explanation Biodegradable substances are materials that can

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Activity 13.5 Class 10 Science

Activity 13.5: NCERT book Science Class 10 Ever wondered what happens to waste after it’s thrown away? Activity 13.5 in the Class 10 NCERT Science book explores how different waste materials decompose, teaching us about waste management and the roles of biological and physical processes. Understanding Waste Decomposition: Activity 13.5 from Class 10 Science Materials

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Activity 13.4 Class 10 Science

Activity 13.4: Ncert book Science class 10 Understanding Ozone Layer Depletion through Activity 13.4 This engaging activity, presented in Chapter 13 of the Class 10 NCERT Science book, aims to enhance our understanding of the chemicals responsible for the depletion of the ozone layer, the regulations to control these emissions, and the recent changes in


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Top Conceptual Questions for Rotational Mechanics

1) If the total external force acting on a rigid body is zero, then
(a) only linear momentum remains constant
(b) only angular momentum remains constant
(c) both linear momentum and angular momentum remains constant
(d) neither linear momentum nor angular momentum remain constant

2) A ball of mass M is tied to a string of length L is whirled round in a horizontal plane in a circle of radius R. The speed of the stone is increased beyond the maximum permissible value and the string breaks suddenly; then
(a) the stone will jerk radially outwards

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Integration of irrational functions

Introduction The integration of irrational functions, which involves incorporating radicals (or root functions) into the integrand, is a challenging yet intriguing area of calculus. These functions often contain variables under a square root or higher-order roots, such as $\sqrt{x}$, $\sqrt[3]{x^2 + 1}$, and similar forms. This article delves into the methods and applications of integrating

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