B_lambda is the Planck Function 1. Start with the integral on the left and prove the...
Three questions!please! 7. Prove that J(x) is integrable on (0,b), and calculate their integral. 8. Prove that the following function is integrable on [0, 1], and calculate the integral. 1 if for some n E N 0 (z)= otherwise. 8. Prove that if f is integrable on (a, b, then f2 is also integrable on la,b
Prove\:\left(cos\left(?\right)\:+\:sin\left(?\right)\right)^2\:=\:1\:+\:sin\left(2?\right)
Prove:$$ \int_{0}^{1} e^{x} \sqrt{2 x+1}\left(1+x+x^{2}\right)^{100} d x \leq \sqrt{\frac{\left(e^{2}-1\right)\left(3^{201}-1\right)}{402}} $$You may not use any integral computation tools such as Wolfram Alpha for this question. HINT: Think about inner products.
Prove the identity. 2 tane = sin 20 1 + tan 20 verify the identity, start with the left side and transform it to obtain the right side. Choose the correct step and transform the expression according to the step chosen 2 tano 1 tano Y D DOO sin 20
Select the second integral, set the start time to 0, and set the end time to 3 to answer the following questions. (a) What is the value of Son f(x,y) ds for Osts 1? (b) What is the value of f(x,y) ds for 1 sts 2? (c) What is the value of f(x,y) ds for 2 st 3? (d) Using your answers from parts (a) to (c), what is the value of den f(x,y) ds + le f(x,y) ds +...
008 Notes points The table gives the values of a function obtained from an experiment. Use them to estimate f(x) dx using three equal subintervals with right endpoints, left endpoints, and midpoints. 5 67 8 9 (a) Estimatef(x) dx using three eqa subintervals with right endpoints. If the function is known to be an increasing function, can you say whether your estimate is less than or greater than the exact value of the integral? less than e greater than o...
The integral integral_3^9 x^2 dx can be calculated approximately by the left sum method (finding the area of multiple rectangles whose top left corners lie on the curve). Figure 1 shows such an approximation with 4 rectangles. Write a MATLAB function to calculate the truncation error caused by the left sum method for integral_3^9 x^2 dx. Your function should meet the following requirements: It should be named NumericalInt It should have the number of rectangles as the sole input argument....
can you please solve all the questions 4 a) Find fx) dx using the Left-hand Sum. ONote ar is not 2 1 consta) fx) 5.75 9.5 12 14 b) Sketch the rectangles used to evaluste the definite integral in a) 10 Evaluate the definite integral using the Right-hand Sum e) fn The regions A. B, and C in the figure above are bounded by the graph of the function fand the a-axis If the area of each 5. region is...
(d) Use the Integral Inequality to prove that sin (rx(In(x + 1) dx = 1 671 (2) - In(3) - ;) 4
1. Consider the following integral. zde (a) (4 points) Draw a diagram representing La, which is the approximate value of the integral using left endpoints and 4 rectangles. (b) (4 points) Approximate the value of the integral by computing L. You will receive zero points if you do not compute La 2. (2 points) Choose the expression that is equal 1 dr. () lis (+/(2+33'+ (B) Him ? Ž (2+ ?))(2+3)+1 (C.) limivo +1 (D) um 22:10)+1