If in the integrand of an integral, the function is a combination of the functions. tanθ and sec2θ \,a solution method can be the integration by u-substitution. Remember that the derivative of the tangent is the square of the secant. }],...
Secant: By definition, the secant function is the inverse, as a fraction, of the cosine:sect=1cost.. Its integral is not immediate but if its square is, this integral is defined by the tangent. Answer and Explanation:1
Note: to enter θ, type the word theta. ∫ ◻ lθ (C) What is the value of the above integral in terms of θ ? ◻ +C (D) What is the value of the original integral in terms of x ? Note: WAMAP does not recognize ...
I used a tangent substitution instead and ended up integrating secant (with the upper limit changing to pi/2); your integral is analogous. Since the antiderivative involves logarithm of a function which goes to infinity as theta approaches pi/2 , the integral indeed diverges, so the absolute ...
Note: to enter θ, type the word theta. ∫dθ (C) What is the value of the above integral in terms of θ ? longrightarrow+C (D) What is the value of the original integral in terms of x ? Note: XYZ does not recognize t...
Recall the relationship between secant and tangent. The Pythagorean identity that relates the two is {eq}\tan^2 \theta + 1 = \sec^2 \theta. {/eq} The derivatives of each are: {eq}\displaystyle \frac{d}{d\theta} \tan \theta = \sec^2 \theta \\ \displaystyle \frac{d}{d \theta...
We have been given an integrand which is a product of a secant function and a tangent function. We will apply the substitution to evaluate this integral. Then we will apply the limits. Answer and Explanation:1 {eq}\text{Let's evaluate}\\ \int \sec \theta \tan \theta d\theta\\ \tex...
We can integrate by using a trigonometric substitution in terms of secant, or by choosing the square root term as the substitution. This gives us a rational integral to calculate. Answer and Explanation: We calculate this integral by using the substitution {eq}\displaystyle \; u = \sqrt{4x...
The u-substitution method is used in trigonometric integration to calculate integrals of products of powers of tangents and secants or with products of powers of sines and cosines. Answer and Explanation: Given data: We are given the integral: $$\displaystyle \int \tan^5 \th...