To assess your understanding of the indicated learning competencies, perform this learning task. Direction: Use separate sheet of paper for your answers and solutions. Activity 1: Match ME! Matching Type. Match the functions in Column A with their corresponding antiderivatives in Column B. Column A Column B 1. S(ex + 3*)dx a. 4In|x| + c 2. S 5* dx b. 3In|x| + C 3. S 3x+2dx c. 9 3 In3 + C 4. S3 dx 5% Ins + C 5. S 4x-'dx e. ex + 3X + in3 + C Activity 2: Solve each of the integral by showing your complete solution. 1. S 7exdx 4. S 12x+1 dx 2. S(5ex - 6*)dx 5. SEdx 3. S 3(5*) dx 6. J -3x-1dx Analysis: Express what you have learned in these lessons/ activities by answering the questions below. 2. What is an exponential function? A logarithmic function? 3. In what way did theorems/ techniques of antidifferentiation help you find the integral of an exponential function? of a logarithmic function? Assessment: Multiple choice. Read and analyze each statement. Write the letter that best describe your answer. If answer is not found, give the correct one. (3 points each) 1. What is f 5e* dx ? a. 5 ex + C b. ex + C C. = ex + C d. e5x + C 2. Evaluate S e3x dx. a. e3x + C b. =e3x + C C. 3e3x + C d. zex + C 3. Evaluate S- dx. a. Inx + C b. 2 Inx + C c. 2 In 2x + C d. -2Inx + C 4. Evaluate S 5x+1 dx. a. 5 5 In 5 + C C. 5 5+1 - + C In 5 b. 5x 5x+1 In 5 + C d. In 5 + C 5. Evaluate S x2 2+4x) dx . a. 1 + 4 In /x/ +C c. x + 4 In /x/ +C b. 1 + In / 4x/+C d. x + In / 4x/ + C4. To evaluate dx, our first step is to divide 4x into 4x+1. Analysis: Express what you have learned in these lessons/ activities by answering the questions below. 1. In what way did theorems/ techniques of antidifferentiation help you find the integral of a function? Assessment: A. Multiple Choice. Read, analyze, & write the letter of the correct answer on a separate sheet of paper. 1. Evaluate S (3x + 5)dx a. -x2 + 5x b. 3x2 + 5x + C c. =x2 + 5x + C d. 5x2/3 + 5x + C 2. Evaluate S x(9x + 2)dx a. 3x3 + 2x b. 3x3 + x2 + C c. 9x3 + 2x2 + C d. 9x2 + 2x + C 3. Evaluate S (5x4 - 8x3 + 9x2 - 2x + 7)dx. a. =x5 - 1x4 + 4x3 - 4x2 + 7x + C c. x5 + 2x4 - 3x3 - x2 + 7x+ C b. x5 - 1x4+2x3 - 2x2 +7x + C d. x5 - 2x4+ 3x3 - x2 +7x + C 4. What is S Vx dx ? a. xz + C b . SXz + C c. x2 + C d. 2x . 3X2 + C 5. What is S Vx4 dx ? a. 2xz + C b. 2x + C c. 2x3 + C d. 2x3 + C B. Solving. For each of the following, show complete solution. Determine the antiderivative of the following functions. 1. S(3s -2 + s + 2 ) ds 2 . [w s + w + + w5) w ? -) dw 3. S(u2 + u + 1) du 4. S(24 + 3z2 + 1) dz 5. S(-2x5 - 6) dxx-4+1 r-3+1 r-2+1 EL + C= _ _. 1.+c. -4+1 -3+1 -2+1 3x3 2x2 X 5. [( tut tut + v) du = [-vidu+ ju'dv+ judv 1+1 + C = - + -+-+C. 20 3 2 Note: A common mistake in antidifferentiation is distributing the integral sign over a product or a quotient. It is better to rewrite a product or a quotient into a sum or difference. If(x)g(x)dx = Sf(x)dx . Jg(x)dx and fax = [foodx Sg(x)dx To assess your understanding of the indicated learning competencies, perform this learning task. Direction: Use separate sheet of paper for your answers and solutions. Activity 1: Match ME! Match the functions in Column A with their corresponding antiderivatives in Column B. Column A Column B 1. f(x) = 3x2 + 2x + 1 a. F(x) = 3x3 - x 2. f(x) = 9x2 - 1 b. F(x) = x3 + x2 +x 3. f(x) = x2 -2 C. F(x) = 2x2 - 3X3 4. f(x) = (x + 1)(x -1) d. F(x) = -2x2 + =x3 5. f(x) = x(4 - x) e. =x3 - 2x + 1 6. f(x) = x(X - 4) f. 3x3 - x +1 Activity 2: True or False. Write TRUE if the statement is true, otherwise write FALSE. 1. If F(x) is an antiderivative of f(x) and c is any constant, then F(x) + c is also an antiderivative of f(x). 2. If F is an antiderivative of f, can we write it in the form of | f(x)dx = F(x) + C? 3. The expression F(x) + C is called the general antiderivative of f. The constant C is called the constant of integration