View the step-by-step solution to:

Question

1a.jpg1b.jpg

/>

The pictures that I attached are the questions and what I thought about the answers.

1a.jpg

1. a ) Evaluate the definite integral
tan ( x ) dx.
170 14
RC 14
tankx) dx = Jo
sincx )
COS(X )
dx =
since) du
O
u - sink
Let u= cosx
TC / 4
du = - sin x dx
= -
Is due = - Inlul to
du
- sin x
= dx
= - In / cos ( TC / 4) 1 - ( Inicosco) 1 )
= - In 7 + In(1 )
= - In 12
b ) Suppose that g(x) is a continuous function such that q(x) dx = 5.
Evaluate [7 / 4
( g ( tancx ) ) . sec ( x ) + g ( sec ( x ) ) . tan(x ) ) dx .
I'm not sure if I'm thinking right ..
I thought gox) dx = 5 satisfy an even function,
Therefore ,
Even
odd
16/ 4
( g ( tan ( * ) ) . sec (x ) + 9 ( sec( x) ) . tan(x ) ) ax
(ox secex ) + 5 tan(x ) ) dx
76 14
1 14
=
5 tan ( x ) dx = - 5 /n/ cos ( x ) |
1 - TC / 4
-1 14
= -5/n 7+5/n /cos (7/4)1
= 0 "70

1b.jpg

C ) Let fax) be a strictly increasing differentiable function such
that fox ) > O for all x. Define get) = fox) dx. To estimate
the integral [ = / "get ) dt .
Alice uses a trapezoid sum with 10 parts, and Bob uses a
left- endpoint Riemann sum with 10 parts. Whose estimate is
bigger and why ?
Loft sum = foxo JAX, + fox, Jox2 + .. + fCan-1Jaxn
4X = 6-a _ 10= 1 x= 0, 1. 2, 3, 4. 5. 6, 7, 8, 9, 10
10
[ = gco). 1 + 9(1). 1+ 9(2). 1+ 9 (3). 1 +... + 9(9). 1
Trapch ) = Left (n ) + Right (n )
2
I know from the theory that the trapezoid rule is better
that the left or right rules ( Midpoint rule is the best)
so left-endpoint sum is bigger, but how do I show
algebracally ? ? ?

Top Answer

View the full answer
New Doc 2019-08-05 15.08.00_1.jpg

La is absolutely
write fight 4 you well
define to write.
1 (b )
9 ( x ) a v = 5
4
g ( tanx ) sec an) + g ( sec's)
414
. tank ) dn
g (m) dy = 5 a constant
not affected by odd or
even function
Now...

Sign up to view the full answer

Why Join Course Hero?

Course Hero has all the homework and study help you need to succeed! We’ve got course-specific notes, study guides, and practice tests along with expert tutors.

-

Educational Resources
  • -

    Study Documents

    Find the best study resources around, tagged to your specific courses. Share your own to gain free Course Hero access.

    Browse Documents
  • -

    Question & Answers

    Get one-on-one homework help from our expert tutors—available online 24/7. Ask your own questions or browse existing Q&A threads. Satisfaction guaranteed!

    Ask a Question
Ask a homework question - tutors are online