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Integration of fractional part of x For example, to integrate the fractional part function from a to b, where a and b are real numbers and a < b, you would do the following: For a general formula, if a and b are not integers, you would need to calculate the integrals over the first […]
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Integrating a constant is a fundamental concept in calculus. When you integrate a constant ( c ) with respect to a variable ( x ), the result is a linear function in ( x ). The integration is performed as follows: $$ \int c \, dx = c \cdot x + C $$ Here, (
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The integration of the UV formula, often referred to as integration by parts, is a technique used in calculus. It is based on the product rule for differentiation and is used to integrate the product of two functions. The formula is expressed as: $$ \int u \, dv = uv – \int v \, du
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Number 18 is a composite number and we will find how to find the factors of 18. We will also see techniques to find out the Prime factorization of 18 easily Factors of 18 A factor of a number is an exact divisor of that number. So factors of 18 are the numbers which are
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Number 12 is a composite number and we will find how to find the factors of 12. We will also see techniques to find out the Prime factorization of 12 easily Factors of 12 A factor of a number is an exact divisor of that number. So factors of 12 are the numbers which are
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The integral of the log function, $log x$, can be found using integration by parts. The integral of $\ln x$ with respect to (x) is: \[\int \ln x \, dx = x \ln x -x + C\] Here, (C) represents the constant of integration, which is added because the process of integration determines the antiderivative
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Here are Last minute preparation tips for board exams
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The derivatives of the hyperbolic functions are quite straightforward and somewhat analogous to the derivatives of their trigonometric counterparts. Here are the derivatives for the six primary hyperbolic functions: (1) Hyperbolic Sine $sinh$:$$\frac{d}{dx} \sinh(x) = \cosh(x)$$The derivative of hyperbolic sine is hyperbolic cosine. ProofThe hyperbolic sine and cosine functions are defined as follows: $$\sinh(x) =
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