For any integer n geq 2,let I_n = int tan^n x | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) We are given $I_n = \int 	an^n x \, dx$. We can rewrite the integral as: $I_n = \int 	an^{n-2} x \cdot 	an^2 x \, dx$ Using the identity $	an^

Vedclass · Accepted Answer

$(n-1, 1)$

Vedclass · Answer

(A) We are given $I_n = \int 	an^n x \, dx$. We can rewrite the integral as: $I_n = \int 	an^{n-2} x \cdot 	an^2 x \, dx$ Using the identity $	an^2 x = \sec^2 x - 1$,we get: $I_n = \int 	an^{n-2} x (\sec^2 x - 1) \, dx$ $I_n = \int 	an^{n-2} x \sec^2 x \, dx - \int 	an^{n-2} x \, dx$ For the first integral,let $u = 	an x$,then $du = \sec^2 x \, dx$. Thus,$\int 	an^{n-2} x \sec^2 x \, dx = \frac{	an^{n-1} x}{n-1}$. Substituting this back,we have: $I_n = \frac{	an^{n-1} x}{n-1} - I_{n-2}$. Comparing this with the given form $I_n = \frac{1}{a} 	an^{n-1} x - b I_{n-2}$,we identify: $\frac{1}{a} = \frac{1}{n-1} \implies a = n-1$ $b = 1$ Therefore,the ordered pair $(a, b)$ is $(n-1, 1)$.

For any integer $n \geq 2$,let $I_n = \int \tan^n x \, dx$. If $I_n = \frac{1}{a} \tan^{n-1} x - b I_{n-2}$ for $n \geq 2$,then the ordered pair $(a, b)$ equals to

Similar Questions

For any integer $n \geq 1$, the number of positive divisors of $n$ is denoted by $d(n)$. Then, for a prime $P$, $d(d(d(P^7)))$ is equal to

Pollen grains of a plant,whose $2n = 28$,are cultured to get callus by tissue culture method. What would be the number of chromosomes in the cells of the callus?

$A$ bar of cross-sectional area $A$ is subjected to two equal and opposite tensile forces at its ends as shown in the figure. Consider a plane $BB'$ making an angle $\theta$ with the length. The ratio of tensile stress to the shearing stress on the plane $BB'$ is

If there were no gravity,which of the following will not be there for a fluid?

Which enzyme stimulates the germination of barley seeds?

Vedclass Test Series

Exam Paper Generator

Online Exam Module