Evaluating an Integral In Exercises 1 and 2, evaluate the integral.
∫
0
3
x
sin
(
x
y
)
d
y
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
Expert Solution & Answer
To determine
To calculate: The value of the integral given as ∫03xsin(xy)dy.
Answer to Problem 1RE
Solution:1−cos(3x2)x
Explanation of Solution
Given: The provided integral is ∫yy2xy+1dx.
Formula used: The integral property of trigonometry given as:
∫sin(ax)dx=−cos(ax)a
Calculation: The function is integrated with respect to y, taking x as a constant variable:
sinx
cosx - e
+e sinx +*
The
integral
dx may be written as me
nsinx
+px+ qe™ + C,
sinx
where m, n, p, q, r, and C are constants not equal to zero. Evaluate m+n+p+q +r.
sinx +x
sinx
+e
COsx - e
The integral
dx may be written as me
nsinx
+px+qe"* + C. where m, n, p, q, r, and C are constants not equal to
e sinx
zero. Evaluate m +n+p+q+r.
A -5
B 5
D) 3
Fill-in the blank. Evaluating the integral f
+x+1 dx equals (x + _+ C)
x2 +1
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