Question

Q1 dx, 115 5xita dx. 2) ſ tan°4x dx . 3) 06-341 S[cos(x? 4) + 1) + xdx, 5) prove that I cscu du = -Inlcscu + cotul + c x2 + Q2 r3 dx 1) dx 2) sino cosºede , 3) /* sec°8 de , 4) * sec`e do , 4) , Port + 4 1 5) dx . 4- x2) 4 Q3 Answer A or B (graph the functions) A-Determine the area of the region enclosed by y = sin x, y = cos x,x=TT /2 and the X axis. B- Determine the area of the region enclosed by the two curves x* =yand y=2- Q4 For the matrix [A]. 1 [A] = secx 2 tan'x 2 Find: 1- The transpose of this matrix then find the value of the determinant of this transpose. 2- The cofactor of as and a23 Q5 Find the value of x, y and z for the following linear equations. x + y = -3, y + z = 3, X-y-z = 6 - L 2 -3 ONS

Answer 1

J 5x2 + 4 22*45 - I den a²+x2 a 3 5 I tom (12.145) ac 2 3 255 ten so. Jedan ( 215 )46. 57244 where C - Integrasing constant, 2. Stan 4x dhe (see 4.x) - 1) che Simee 2 ton a= See²a-1 I see? Anda - Sche -x+ J see u du put +C 4 a s seruau te 4x=4 Oro 4 dhe du des 4. Sinee I see ideea a temu te. axt tam u to tem (4x) + c 50, Stam (40) dh ont e tem (4) - Integranny where Constent,

3. 5-3x2 11 put بان 02 V3 12 a 2 1 at 11 Since sim'z +6 t sin ve + c Inc So. de a a Sin + С. 5-3x2 where es Integrating constant. a. s (cos (1²+1) + put Soos 2 + 1 ) 2 2 2 22 dx 2 dl Coszaq t n a dx a de 2 2 inz + c (A) = 2 101214 + = 2 sim (5+1) + 1 / 2 1 (2²+1) + c so, sport cali) 4 ans) jisto (ala)* y) Ion (932) 4 , SimZt 19 Ź where - Integrasing constant

sh ese u du eseu du rescu a cot u) (esen teot u) dz Dut eseut cotu a z im =d2 যত csculescu + cotu) du sraz (- eseu esta escul de in dot un esculte jese u du = - in/cot. ut ese ul nc Intessaning Soo where C = Intessani constent,