Antiderivative Of Tanx Antiderivative Of Tanx
For finding the Antiderivative of tanx we will use some identities of trigonometry, substitution method and the log identities the antiderivative of tanx is also known as Integration of tanx. To get the antiderivative tanx use the trigonometric identity tanx = 1/cotx = sinx/cosx. This implies that tanx = sinx/cosx ( since tanx = sinx/cosx ). It means ∫ tanx dx = ∫ sinx/cosx dx Now use the substitution method of integration for cosx Let cosx = t by differentiating it we get - sinx dx = dt Put the value of sinx and dx in above integral equation we get Such that ∫ tanx dx = ∫ sinx/cosx dx = - ∫1/t dt It implies that ∫ tanx dx = ∫ sinx/cosx dx = - logt +c Where c belongs to a constant By substituting the value of t in the equation we will get ∫ tanx dx = ∫ sinx/cosx dx = - log(cosx) + c Therefore we get ∫ tanx dx = ∫ sinx/cosx dx = - log(cosx) + c Know More About Probability Worksheet
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As we know the logarithmic identities like Log m +log n =log (m*n ) Log m – log n = log (m/n) Log mn = n log m So we can say -log (cosx ) can be written as log (1/cosx ) Which can further be written as log (secx) since we know that 1/cosx = secx Therefore log (1/cosx ) = log (secx) So we can say that the antiderivative of tanx can be written as ∫ tanx dx = - log(cosx) + c = log (secx ) +c Where, c is the constant. So, finally we get the result that antiderivative of tanx = -log(cosx) +c where c belongs to a constant. as we seen the antiderivative of tanx become quite easier by the method we used known as substitution method. By other method may be the antiderivative of tanx is quite typical and confusing. An antiderivative can be defined as an operation opposite to differentiation operation or we can say that to find antiderivative of a function we have to find the integral of that function. Suppose we have a function f( x ) the we will integrate it to find its anti derivative therefore we get ∫ f( x ) = g( x ), therefore g( x ) is the antiderivative of function f( x ). If we will differentiate g( x ) that is d( g ( x ) ) / dx we will get f( x ) which is our original function. This is how we can find antiderivatives. Solving Initial Value problems in Antiderivatives Antiderivative is the term used in the calculus mathematics and especially in the topic of the Differential Equations. Read More About Properties Of Numbers Worksheets
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The anti derivatives are the type of the integral equations in which we don’t have limits on the Integration symbol. It is the reverse process of the derivatives or we can say it as the process of reverse differentiat. Antiderivative and Indefinite Integrals What anti derivatives are and what are the indefinite integrals in the calculus? We will also go through the relationship between the Antiderivative and indefinite integrals. Let’s move to the topic with the introduction of the anti derivatives.The normal Integration is called as the anti derivative. We can also understand the anti derivative. Applications of Antiderivatives Anti derivative of function f is the function F whose derivative is function f. We can understand it by an equation as F'=f. This process is also known as anti differentiation. This term is related to the definite integrals by using the functions of calculus. It can be understand by an example as the function F(x)=x3/3 is an anti derivative of the function.
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By substituting the value of t in the equation we will get ∫ tanx dx = ∫ sinx/cosx dx = - log(cosx) + c Therefore we get ∫ tanx dx = ∫ sinx/...