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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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Examination time is intense, with many students dedicating themselves to round-the-clock study sessions to achieve high scores and move up to the next class. While it’s crucial to put in the effort, it’s equally important to manage exam-related stress effectively. Remember, it’s just an exam at the end of the day! Here are some practical
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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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Integration of sec x can be found using various integration technique like integration by substitution, Integration by partial fraction along with trigonometric identities. The various formula for integration of sec x are I \[\int \sec(x) \, dx = \ln | \sec(x) + \tan(x) | + C\] II \[\int \sec(x) \, dx = -\ln | \sec(x)
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Integration of tan x can be found using various integration technique like integration by substitution along with trigonometric identities. The formula for integration of tan x is \[\int \tan(x) \, dx = \ln |sec(x)| + C\] Proof of the Integration of tan x Integration of tan x can be solved using integration by substitution as
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