Solution : Let I = \(\int\) x\(tan^{-1}x\) dx By using Integration by parts rule, Taking tan inverse x as first function and x as second function. Then, I = (\(tan^{-1}x\)) \(\int\) x dx – \(\int\){\({d\over dx}\)(\(tan^{-1}x\) \(\int\) x dx} dx I = (\(tan^{-1}x\))\(x^2\over 2\) – \(\int\)\({1\over 1 + x^2}\) \(\times\) \(x^2\over 2\) dx \(\implies\) I […]
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Here you will learn what is the formula for volume of cube, its derivation and examples based on it. Let’s begin – Formula for Volume of Cube Let the side or edge of the cube be a, Then the Volume of Cube = side \(\times\) side \(\times\) side = \(a^3\) Also Read : Formula for
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Here you will learn what is the formula for volume of cuboid, its derivation and examples. Let’s begin – Formula for Volume of Cuboid suppose, the length of cuboid is l, breadth of cuboid is b and height of cuboid is h. Then Volume of Cuboid = l \(\times\) b \(\times\) h Also Read :
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Here you will learn formula for surface area of cube (total surface area and lateral surface area), its derivation and examples. Let’s begin – What is Cube ? A cube is a cuboid which has all its edges or sides equal i.e length = breadth = height = s (side of cube). Formula for Surface
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Here you will learn formula for surface area of cuboid (total surface area and lateral surface area), its derivation and examples based on it. Let’s begin – What is Cuboid ? A cuboid is a three dimensional box. It is defined by the virtue of its length l, breadth b and height h. It can
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Here you will learn concept of gcd ot hcf and how to find greatest common divisor or highest common factor of numbers and fractions with examples. Let’s begin – Concept of GCD or HCF Consider two natural numbers \(n_1\) and \(n_2\). If the numbers \(n_1\) and \(n_2\) are exactly divisible by the same number x,
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Here you will learn concept of LCM and how to find least common multiple (LCM) of numbers and fractions with examples. Let’s begin – Concept of LCM Let \(n_1\) and \(n_2\) be two natural numbers distinct from each other. The smallest natural number n that is exactly divisible by \(n_1\) and \(n_2\) is called Least
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Here you will learn what are rational and irrational numbers with examples. Let’s begin – What are Rational and Irrational Numbers ? Rational Number A rational number is defined as number of the form a/b where a and b are integers and b \(\ne\) 0. The set of rational numbers encloses the set of integers
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Here you will learn what are prime numbers in math, its properties and method to check whether a number is prime or not. Let’s begin – What are Prime Numbers in Math ? A natural number larger than unity is a prime number if it does not have other divisors except for itself and unity.
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Here you will learn how to find square root and cube root of a number and properties of squares and cubes. Let’s begin – Square Root and Cube Root (a) Square and Square Roots When any number multiplied by itself, it is called as the square of the number. Thus, 3 \(\times\) 3 = \(3^2\)
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