IV. Problem Solving: A. Write the expression as a single Integral 1 . I f ( x )ax + fir ( x )dx = PAGE 151 2. fo f( x ) dx - S, f ( x)dx = 3 . So f(x)dx + f f( x )dx = 4. [ f(x)dx + f f (x)dx = 5. So ((x)dx - S' f(x)dx =_ B. Assume that f, f(x)dx = 3 and Jig(x)dx = -2, find the following: 1. ['If (x) + g(x)]dx = 2. [ [2f (x) - g(x)]dx = 3. [If (x) - 8(x)]dx = 4. [*149 (x) - 3f (x)] dx = 5. ['If (x) + 3g(x) ] dx =PAGE 150 3. For the enclosed regions bounded by y = x - 6x and y = -2x in the graph, what is the integral that describes the enclosed regions? A. L, (x' - 6x) dx B. L. (x] - 6x - 2x) dx C. ; (x- 6x) dx + 5 -2x dx D. [, (x] - 4x ) dx + Jj(-x]+ 4x) dx 4. What is the area of the enclosed regions in problem number 3? A. 10 sq. units C. 8 sq. units B. 12 sq. units D. 4 sq. units 5. Given the Jo x'dx, which of the following is the integrand? A. 0 C. x B. 2 D. dx Ill. Matching Type: Match the definite Integral in column A with its value in column B. Letters only. A B 1. . (2x - 3) dx A. -2 2. [ (x3 + 2x) dx B. 0 3. [(x2 - 2) dx C. 4. Jo(x3+ 3x - 1) dx WIN D. [ (4x -2) dx E. 2 6. [[(y+ 1) -(2-1)]dy F. 3 7. [.(vx - x] ) dx G. 5 8. [(1 - x7 ) dx H. 8 9. J. 2 dx 10. foy dy J.NAME: GRADE & SECTION: PAGE 149 General Instructions: This Is a Quiz worth 30 points from module 8. Cut this part (broken lines) and staple them properly and submit them in school or (this is encouraged) take clear pictures or scan your answer sheets and upload them to GENYO. Don't Forget to write your name grade and section on the upper left comer of the next pages. ALL final answers should be written in blue or black ink only. Strictly NO any kind of ERASURE or change in answer, NO superimposition on final answers. Write your answer here. Detach the pages of this quiz and submit them together with your other assessments on the date of submission. (30 points) I. True or False: Write True if the statement is always correct, otherwise write False. 1. All continuous functions have antiderivatives. 2. If f and g are continuous on a s x s b, then [auf(x) + g(x)]dx = ] f(x)dx - leg(x)ex 3. The approximation of area is more accurate if n is increased. 4. [ f(x)dx = F(a) - F(b), where F is an antiderivative of f. 5. [ x dx = - ; x dx Il. Multiple Choice: Read and understand the statements, then choose the correct answer. Write the letter of your answer on the space before each number. 1. What is the integral that describes the enclosed region between y = 4x - x* and the x - axis ? A (4x - x2) - x]dx B. [[4x - x]dx c. If x2 dx D. . [4x - x]] dx 2. What is the area of the enclosed region In problem number 17 A. 10.67 sq. units C. 24 sq. units B. 21.33 sq. units D. 25 sq. units