\int^\pi_0 \sin^4(3x) dx Evaluate the integral. \int \frac{sinx}{13+cos^2x} dx Evaluate the following integral: \int_{0}^{1} \dfrac{x^3}{\sqrt{9-x^2 dx. Evaluate the integral: integral_{0}^{2} 2x^2 + 2x + 3 / (x^2 - 4) dx. Evaluate the integral \int s...
Answer and Explanation:1 Given: $$\displaystyle \int_{-1}^1 \dfrac{e^{\arctan (y)}}{1 + y^2} \, dy $$ Let us assume that: $$u = \arctan (y) \hspace{1 cm} \text{(Eq... Learn more about this topic: Definite Integrals: Definition from...
Integral of (dx)/(x^2 sqrt(x^2 - 16)), x = 4 sec(theta). Evaluate the integral \int_{0}^{\pi} \sin^3(5x) dx Evaluate the integral: 6+sinx over cos2 x Evaluate the integral of 1/(x^2*sqrt(9 - x^2)) dx using trigonometric substitution. Evaluate: integral ...
Use a power series to approximate \int_{0}^{0.4}\ln (1 + x^4) dx to six decimal places. Find the Maclaurin series of sinx. Use this series to obtain the 15^{th} degree polynomial of \sin(x^3) and approximate the integral \int^1_0 \sin(x^3) dx to ...
integral_0^infinity x^5 e^{-2 x} dx Evaluate the integral of cos(sqrt x) dx. Evaluate the integral of (x^2+4x)/(x^3+6x^2+5) dx. Evaluate: Integral of \cot 2x dx. Evaluate the integral of x^5 (x^6 - 4)^9 dx. Evaluate the integral int_0^2int_y^2y (1...
Evaluate the integral: int_{-2}^{0} int_{-Square root{4-x^2^{0} 8xy dy dx Evaluate the integral \int_0^{\frac {2\pi}{3\frac {5\sin(\theta )+5\sin(\theta )\tan^2(\theta )}{\sec^2(\theta )}d\theta. Evaluate the integral: \iint_{D}^{}xsinx(x+y)dA, with ...
A straightforward method for the synthesis of 5-substituted tetrazolo[1,5-a]pyrido[2,3-e]pyrimidines from 2,4-diazidopyrido[3,2-d]pyrimidine in SnAr reactions with N-, O-, and S- nucleophiles has been developed. The various N- and S-substituted products were obtained with yields from...
Is the following true or false? d^2/dx^2 (x^2cosx) = 2cosx - 4xsinx - x^2cosx Summation (n = 0 to infinity) ((-1)^n)5 by 4^n) = 4. True or false? Summation (n = 1 to infinity) (((-1)^(n-1))(2^(n-1))) by (5^(n-1)) = 5 ...
(a) \lim_{x\rightarrow \infty}\frac{x^2}{e^{3x} + x^3 + 1} (b) \lim_{x\rightarrow 0^+} (cot x)^{sinx} Find the following limits by L'Hospital's rule (a) lim_{x \rightarrow 0^+} (tan x - x)/x (b) lim_{x \rightarrow \infty} ln x/\sq...
Evaluate integral_{-2}^5 (2x^2 - 3x + 7) dx. Evaluate \int^{(1,π)}sin(y)dx+(xcos(y)-sin(y)) dy Evaluate: \int_0^{\frac{\pi}{2 \sin^4 x \cos^x 4xdx Evaluate: sum^{infinity}_{k = 1} [3/4.(2/3)^k - 1/2.(1/3)^k] Evaluate summation_{i = 1}^n ...