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: $$\sinh(x) =
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Integrating hyperbolic functions is similar to integrating their trigonometric counterparts, but there are some key differences due to the properties of hyperbolic functions. Here are the basic integrals for the six primary hyperbolic functions: (1) Sinh (Hyperbolic Sine):$$\int \sinh(x) \, dx = \cosh(x) + C$$The integral of hyperbolic sine is hyperbolic cosine. ProofTo integrate$\sinh(x)), we
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Hyperbolic functions are analogs of the ordinary trigonometric, or circular, functions. They are defined in terms of the exponential function and are important in many areas of mathematics, including algebra, geometry, calculus, and complex analysis. Hyperbolic functions are closely related to the exponential function, as evident from their definitions. The basic hyperbolic functions are: Definition
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Choosing an engineering college in India is a significant decision that can impact your career path and personal development. Here are some key factors to consider when making your choice: How to choose your engineering college Just scoring well in JEE Main is not enough. What is important is to choose the right field of
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The JEE Main exam will have two papers- the first paper will have equal questions from physics, maths and chemistry with equal weightage for all the subjects for B.E. and B. Tech exams. The second paper will have Maths, aptitude test and drawing for architecture and planning candidates. Some important tips to score well in
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First lets us see what is Modulus function and then we will see how to do Integration of modulus function What is modulus function Modulus Function is defined as the real valued function $f : R \rightarrow R$ , y = |x| for each $x \in R$ For each non-negative value of x, f(x) is
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